NEWLY    REVISED    EDITION   OF 

RICHTER'S 
MANUAL  OF  HARMONY 

A 

PRACTICAL  GUIDE  TO  ITS  STUDY. 


PREPARED    ESPECIALLY    FOR   THE    CONSERVATORY 
OF    MUSIC   AT    LEIPSIC 


Ernst  Friedrich  Richter. 


REVISED   AND   EDITED   FROM   THE   LATEST  EDITION 
BV 

OSCAR  COON, 

WITH   EXPLANATORY   NOTES  AND   ADDITIONAL  EXERCISES. 


New  York  : 

CARL    FISCHER,    Publisher, 
6,  8,  AND  lo  Fourth  Avenue, 


v^^> 


Copyright,  1896,  by  Carl  Fischer. 


f,  N.  OILiON  OOUrANV, 

PRINTEIIS   AND   BOOKtlNDCM^ 

aOITON,   U.   t.  A. 


EDITOR'S    PREFACE. 

That  Richter's  Manual  of  Harmony  is  one  of  the  best  text-books 
ever  written  on  the  subject,  no  one  will  now  deny.  In  1843,  Richter 
became  professor  of  harmony  and  counterpoint  in  the  Conservatory 
of  Leipsic,  and  this  work  is  the  result  of  his  experience  as  a  teacher 
in  that  institution.  The  twelfth  edition  was  published  as  early  as 
1876,  and  the  work  has  been  translated  into  Dutch,  Swedish,  Italian, 
Russian,  Polish  and  English.  The  enormous  success  of  the  work  be- 
comes apparent  when  we  reflect  that  it  has  passed  through  its  twen- 
tieth German  edition. 

In  preparing  this  edition  of  the  manual,  the  editor  has  endeavored 
to  make  the  language,  which  in  other  editions  is  often  somewhat  ob- 
scure, more  explicit  and  to  the  point.  Pupils  frequently  complain 
that  they  cannot  catch  the  meaning  of  many  of  the  explanations. 
The  reason  is,  that  they  are  not  sufficiently  advanced  in  musical  know- 
ledge to  enable  them  to  comprehend  the  meaning  of  the  prolix  lan- 
guage used.  .Students,  and  especially  those  who  have  not  the  advan- 
tage of  a  teacher^  require  clear  and  concise  directions.  Having  used 
this  manual  many  years  as  a  text-book  in  teaching  harmony,  the  ed- 
itor has  learned  by  experience  where  the  difficulties  lie,  and  has  done 
what  he  could  to  remedy  them.  Many  additional  exercises  have  been 
appended  to  the  work  and  also  some  notes  of  explanation. 

The  Editor. 


m21()1.8*? 


FROM  THE  PREFACE  TO  THE  FIRST  EDITION. 

The  reason  for  publishing  this  manual  of  harmony  is  given  in  the 
title.  During  the  course  of  studies  in  the  theory  of  music,  it  was  de- 
sirable to  furnish  the  pupils  with  some  aid  in  explaining  and  illustrat- 
ing the  principles  brought  before  them.  The  qualities  of  such  a  work 
the  author  believes  to  be  these : 

//  must  contain  the  essential  fundamental  principles  of  musical 
theory  in  the  most  concise  and  complete  form  possible;  that  these 
principles  jnust  be  accompanied  by  practical  directions  for  their  ap- 
plication in  order  to  qualify  for  future  attempts  in  composition. 

The  book  contains  no  scientific  theoretical  treatise  on  harmony,  so 
to  speak,  but  (  as  with  any  system  of  harmony  it  rests  upon  a  firm 
basis  )  is  devoted  only  to  the  practical  object,  which,  with  the  scanty 
means  now  accessible,  would  be  difficult  to  obtain  in  an  abstractly 
scientific  manner. 

There  has,  indeed,  always  been  a  disposition  to  inquire  after  mathe- 
matical precision  in  musical  rules,  and  especially  among  the  young, 
opposed  to  authority,  who  wish  to  have  everything  so  clear  that  doubt 
would  be  impossible,  yet  shrink  from  learning  the  beauties  of  this 
beautiful  art  by  means  of  the  anatomical  knife ;  and,  it  is  not  to  be  de- 
nied that  in  this  regard  there  is  a  want  in  musical  literature  which  has 
not  yet  been  fully  supplied.  All  attempts  of  this  kind  have  so  far  failed 
to  produce  a  really  tenable  scientifically  musical  system,  according  to 
which  all  phenomena  in  the  world  of  music  can  be  shown  as  the  nec- 
essary result  of  one  fundamental  principle.  What  philosophers, 
mathematicians  and  physicists  have  achieved  in  this  regard  is  worthy 
of  attention,  but  is  on  the  one  hand,  too  much  divided  to  form  a  com- 
plete whole,  and  on  the  other,  too  abstract,  serving  music  less  than 
other  purposes;  and  notwithstanding  the  knowledge  of  musical  tilings 
shown,  has  but  little  reference  to  that  which  is  really  musical,  which 
is  of  the  most  importance  to  th-  musician  after  all.  What  is  laid  down 
in  musical  text-books  as  a  scientific  basis  has  thus  far  not  been  jus- 
tified, partly,  because  as  the  result  of  learned  individual  investigation, 
it  was  impossil)le  to  form  a  complete  system  with  indisputable  con- 
clusions, and  partly,  because  as  a  fanciful  structure,  it  was  entirely 
(iv) 


without  scientific  support.  (^'The  Nature  of  Harmony  and  Metre," 
by  M.   Ilauptmann,  might  supply  a  palpable  want.) 

Still,  properly  considered,  this  deficiency  is  felt  only  by  the  riper 
and  more  cultivated  musician  who  likes  to  busy  himself  with  theory ; 
not,  however,  so  detrimental  to  the  advancing  student  that  his  pro- 
gress must  suffer  in  consequence  of  it ;  and  the  above  mentioned 
skepticism  might  be  regarded  in  a  certain  way  like  the  childish  de- 
sire to  learn  the  cause  of  everything  by  questions  which  can  seldom 
be  answered  clearly  enough  for  his  stage  of  learning. 

At  first,  the  student  of  music  has  to  devote  his  whole  attention  to 
his  technical  studies,  as  it  will  cost  him  time  and  trouble  enough  to 
reach  the  standpoint  from  which  he  may  more  easily  advance  to  the 
position  of  an  artist.  Here  the  question  is  not  ivhy^  but  rather  hoiv^ 
to  learn  from  experience  and  the  best  models  the  necessity  of  certain 
principles,  not  to  calculate  it.  Afterwards,  should  education,  inclina- 
tion and  calling  require,  it  will  be  time  enough  to  reason  out  thexf^jj/, 
and  the  knowledge  derived  from  experience  will  be  an  aid  not  to  be 
despised  in  discovering  the  natural  laws  of  music.  With  this  prac- 
tical aim  in  view,  the  author  has  undertaken  to  give,  in  a  clear  and 
simple  manner,  the  representation  of  harmony,  and  the  results  of  ob- 
servation and  experience  ;  and  as  the  book  was  intented  for  study ^  to 
let  the  principles  which  it  contained  work  through  themselves,  with- 
out wishing  to  attract  a  large  circle  of  readers  through  a  learned  dress 
or  a  winning  form.  It  contains  the  complete  doctrine  of  harmony, 
with  hints  for  a  rational  method  of  working  exercises  for  fixing  the 
same,  and  for  the  skilful  use  of  all  harmonic  fundamental  principles. 
These  exercises  extend  to  the  beginning  of  contrapuntal  studies.  The 
doctrine  of  counterpoint  itself  will  follow  in  a  later  volume  on  the 
same  plan. 

In  conclusion,  still  a  word  to  the  student  of  art,  an  earnest  one,  but 
well  meant.  Our  object  is  to  reach  a  distant  goal ;  it  is  to  produce 
works  of  art.  For  this,  vigorous,  untiring  industry  is  necessary  to 
comprehend  the  fundamental  principles  of  music  and  to  form  that 
which  is  won  and  understood  into  a  living  structure.  They  will  be 
bitterly  disappointed  who  think  to  pluck  the  blossoms  without  learn- 
ing thoroughly  to  know  and  prove  the  technical  requirements ;  who 
cling  to  the  notion  that  the  charm  of  beauty  which  overspreads  a  work 
of  art  would  be  lost  through  the  analysis  of  the  material,  or  that  the 
primary  forms  of  the  latter  could  never  be  developed  into  that  requi- 
site beauty.      Talent  alone,  without  thorough  knowledge,   has  never 


yet  reached  that  point  where  artistic  efforts  are  really  successful. 
Practice  without  knowledge  is  not  artistic  skill,  but  only  the  working 
of  the  instinct,  which  will  make  the  want  of  proper  education  al- 
ways apparent.  The  spiritual  thought  cannot  dispense  with  the  form, 
and  this  must  be  recognized  and  learned.  Even  if  this  comes  with  the 
thought  itself,  still,  it  is  of  more  importance  in  music  than  anything 
else,  to  analyze  the  thought  logically,  to  remodel  it  into  new  forms, 
and  transform  it  in  the  most  manifold  way.  The  knowledge  of  these 
things  and  the  skill  in  their  use  must  be  acquired  by  the  talented  also, 
and  this  can  only  be  done  by  taking  pains  to  recognize  the  musical 
laws,  and  by  seeking  to  imitate  and  further  develop  what  others 
have  long  since  discovered.  Earnest  persevering  work,  and  above  all, 
a  rational  method  of  developing  to  maturity,  and  for  the  creation  of, 
living  works  of  art,  will,  in  connection  with  musical  ability,  surely 
lead  to  the  goal. 

E.    F.    RiCHTER. 


TABLE  OF  CONTENTS. 


PAGE. 

Introduction' — Ititervals        .         .         .         •         •         •         •     ^3 


PART    I. 

THE   FUNDAMENTAL    HARMONIES   AND    THE    CHORDS    DERIVED 
FROM   THEM. 

CHAPTER.  PAGE. 

I.  The  Triads  of  the  Major  Scale  .  .         .         .21 

II.  The  Triads  of  the  Minor  Scale  .  .  .  .42 

III.  The  Inversion  of  the  Triads  .  .  .  •     5^ 

IV.  Harmonies  of  the  Seventh     .  .  .  .  '57 
V.  The  Inversions  of  the  Chord  of  the  Seventh    .     63 

VI.     Secondary  Harmonies  of  the  Seventh  .  .     69 

VII.     The  Inversion  of  the  Secondary  Chords  of  the 

Seventh       ........     S7 

VIII.     The  Chords  of  the  Seventh  in  connection  with 

Chords  of  Other  Degrees        .  .  .  .90 

IX.     On   Chords   of  the  Ninth,   Eleventh  and   Thir- 
teenth ........     98 

X.     Chromatic     Alteration     of     the     Fundamental 

Harmonies;    Altered  Chords  ....    loi 

XI.     On  Modulation  .  .  .  •  .  •  •    ^^5 

(vii) 


CONTENTS. 


PART    II. 

ACCIDENTAL  CHORD    FORMATIONS.     TONES   FOREIGN   TO 
THE   HARMONY. 


XII.  Suspensions      ..... 

XIII.  The  Organ-Point  ;   Sustained  Tones 

XIV.  Passing  Notes  ;    Changing  Notes 
XV.  Passing  Chords        .... 

XVI.  On  the  Means  for  Modulation  . 


PAGE. 
119 

144 


PART    III. 

PRACTICAL  APPLICATION    OF   HARMONIC   EXERCISES    FOR 
THEIR   USE   IN   THE   PURE   HARMONIC    STRUCTURE. 

CHAPTER.  PAGE. 

XVII.  The    Simple     Harmonic     Accompaniment     to    a 

Given  Voice       .         .          .         .          .  .         .166 

XVIII.  Extension  of  the  Harmonic  Accompaniment      .   1S9 
XIX.     On  the  Formation  of  Melody      ....   192 

XX.     On  Development   of  the   Accompanying  Voices   198 
XXI.     The  Exercises  in  Three-Voiced  Movement         .    202 

XXII.  On  the   Two-Voiced  Movement  .  .  .    208 

XXIII.  Harmonic    Treatment     of     a     Given    Voice     in 

Melodic  Form     .......   209 

XXIV.  The  Five-Voiced   Movement  ....  216 
XXV.     The  Six,   Seven  and  Eight- Voiced  Movement    .    221 

XXVI.     On  the  Musical  Forms  of  Close  ....  228 
Index  of    Subjects        ........   233 


INTRODUCTION. 


Of  the  elementary  knowledge  of  music,  an  acquaintance  with 
which  must  be  assumed  before  beginning  the  study  of  harmony,  that 
portion  which  stands  in  the  nearest  relation  to  it,  The  Theory  of 
Intervals^  will  be  briefly  discussed. 

Intervals. 

Interval  is  the  relation  in  which  one  tone  stands  to  another  in  re- 
spect to  distance.  The  distance  between  any  two  tones  is  reckoned 
by  the  number  of  degrees  of  the  diatonic  scale  which  it  contains,  and 
the  interval  formed  by  those  tones  is  named  accordingly. 

Remark.  —  By  diatonic  degrees  is  understood  the  progression  of  tones  formed  by 
any  major  or  minor  scale. 

Thus,  if  G  be  the  lower  note  of  an  interval  and  considered  as  the 
first  degree  of  the  scale,  A  will  be  the  second  degree,  and  the  interval 
G — A  will  be  that  of  a  second.  E  will  be  the  sixth  degree,  and  the 
interval  G — E  will  therefore  be  a  sixth. 


etc. 


Counting  always  from  the  lower  note,  or  first  degree,   the   major 
scale  gives  the  following  result : 

6  7  8 


-(9-  -G>-  -^- 

Unison  or  Prime.    Second.    Third.      Fourth.        Fifth.        Si.Kth.      Seventh.   Octave. 

The  intervals  are  generallv  only  counted  as  far  as  the  octave,   the 

(13) 


I^  MANUAL    OF  HARMONY. 

same  order  being  repeated  for  those  intervals  which  lie  beyond  that 
compass;  thus,  the  ninth  degree  is  considered  as  the  second,  the 
tenth  as  the  third,  and  so  on. 

There  are,  however,  reasons  which  will  be  perceived  hereafter  for 
giving  names  also  to  those  intervals  which  are  greater  than  the  octave. 
All  such  will  therefore  have  two  names,  as  follows : 


Octave.        Ninth.       Tenth.    Eleventh.  Twelfth.  Thirteenth.Fourteenth.Fifteenth. 


Seventh.    Octave. 


When  distances  between  t\\^o  tones  are  greater,  they  are  simply 
brought  down  to  the  lower  octave. 

More  Exact  Designation  of  Intervals. 

It  will  be  seen  that  the  above  series  of  intervals  is  composed  entirely 
of  the  notes  of  the  diatonic  major  scale  of  C,  and  has  always  Xkx&Jirst 
degree  of  that  scale  for  the  lower  note  of  each  intei-val.  It  is,  how- 
ever, easy  to  understand  that  any  other  degree  of  the  scale  can  serve 
as  the  lower  note  of  an  interval,  in  which  case  the  numbers  of  the  two 
tones  forming  the  interval  will  be  changed,  inasmuch  as  the  lower  note 
of  an  interval  is  always  considered  as  \\\&  first  degree.,  and  other  slight 
differences  will  occur. 

In  order  to  obtain  a  clear  insight  into  these  differences,  the  follow- 
ing principles  must  be  carefully  noted  : 

The  above  series  of  intervals,  in  which  the  lower  note  is  the  first 
degree  of  a  major  scale,  while  all  the  other  degrees  of  the  scale  are 
employed  as  upper  notes,  serves  as  the  foundation  for  the  determina- 
tion of  all  intervals.      These  intervals  are  called  major,  some  perfect. 

Any  chromatic  alteration  of  either  of  the  two  notes  which  form  an 
interval,  alters  neither  the  number  of  the  degree,  nor  the  name  of  the 
interval,  but  makes  necessary  a  more  exact  definition. 

If,  for  example,  a  sharp  or  flat  be  added  to  either  of  the  notes  form- 
ing the  fifth,  C— G,  it  remains  a^T/Z/^  still,  hut  a  difi'e rent  fifth  from 
what  it  originally  was. 


i 


^^^^ 


MANUAL    OF  HARMONY.  15 

In  order  to  distinguish  between  the  various  chromatic  alterations  of 
intervals,  the  following  terms  are  used  : 

I .  Primes  (unisons)  ^fourths,  fifths  and  octaves,  which  are  formed 
of  the  notes  of  the  diatonic  major  scale,  and  have  the  first  degree  of 
the  scale  for  the  lower  tone,  are  called  perfect.  All  the  other  inter- 
vals of  the  same  scale  are  called  major. 


Perfect.  Major.     Major.    Perfect.    Perfect.    Major.    Major.    Perfect.  Major. 


^ 


^_  ,  _  -'9-         -<^-         "1^"  '^' 

PHme.    Second.    Third.     Fourth.      Fifth.        Sixth.  Seventh.  Octave.     Ninth. 

2.   If  the  upper  tone  of  a  major  interval  be  chromatically  lowered 


half-step,  a  minor  interval  is  formed. 


i 


Minor.  Minor.  Minor.  Minor.  Minor. 


-\>^.  ^-f-  -i9-  -&-  -^- 

Second.  Third.  Sixth.  Seventh.  Ninth. 

3.   If  the  upper  tone  of  the  prime,  secmid,  fourth,  ffth,  and  sixth 
be  chromatically  raised  a  half-step,  augmented  intervals  are  formed. 


Augmented.    Augmented.      *Augmented.       Augmented.       Augmented. 


4,  By  raising  the  lower  tone  of  the  minor  third,  perfect  fourth^ 
perfect ffth,  viinor  seventh,  and  perfect  octave,  a  chromatic  half 
step,  diminished  intervals  are  formed. 

Diminished.       Diminished.       Diminished.       Diminished.        Diminished. 


i 


=fer -p.  p. ^. 1^ 

Third.  Fourth.  Fifth.  Seventh.  Octave. 

Remark.— Diminished  primes,  seconds,  sixths  and  ninths  are  harmonically  incon- 
ceivable, but  may  exist  in  melodic  relations  —  in  reference  to  progressing  intervals, 
but  not  to  those  which  sound  together. 


♦Augmented  thirds,  sevenths  and  ninths  do  not  occur   in  harmonic  relations,    .\ugmented 
octaves  are  to  be  regarded  as  augmented  primes. 


I6 


MANUAL    OF  HARMONY. 
Remark  on  the  fortnation  of  Jtitervals. 


The  reason  why,  in  the  formation  of  the  diminished  intervals,  the  lower  tone  was. 
raised,  notwithstanding  that  a  similar  interval  would  result  if  the  upper  tone  were 
lowered,  lies  in  the  peculiar  relations  of  all  intervals  in  respect  to  their  inversion,, 
which  will  be  spoken  of  hereafter. 


General  View  and  Classification  of  Intervals  most  in  use. 


i 


1F 


-K 


Perfect.  Augmented. 


Major. 


->9-       ^^  -&- 

Minor.  Augmented. 


i 


n 


m 


r^ 


:«*: 


Major. 


-P^ 


Diminished.        Perfect. 


■r 


Augmented.    Diminished. 


i 


~m 


■^ 


-¥- 


±t 


Augmented.     Diminished. 


Major. 


Augmented. 


i 


a 


:?r 


1^ 


1^ 


Majc 


Minor.    Diminished. 


Diminished.        Major. 


Division  of  Intervals  into  Consonances  and  Dissonances. 

By  the  expression  consonant  and  dissonant  intervals,  we  do  not 
understand  such  as  do  or  do  not  sound  well,  as  the  terms  might  seem 
to  imply,  but  by  the  former  is  meant  those  which  produce  a  final  and 
complete  effect  on  the  ear  by  themselves,  and  by  the  latter  those  which 
require  to  be  followed  by  another  harmony,  without  which  their  effect 
would  be  unsatisfactory  and  incomplete. 

Consonances  are  all  those  intervals  called  perfect^  and  also  the 
major  and  nihior  thirds  and  sixths. 

The  first  are  called  complete,  the  last  incomplete  consonances. 


MANUAL    OF  HARMONY. 


'7 


The  dissonances  comprise  \.\\q  major  and  minor  seconds.,  major  and 
minor  sevenths^  and  all  the  angmented  and  diminished  intervals. 
The  following  table  gives  a  general  view : 

I.  CONSONANCES. 

a.   Complete. 

The  periect  prime,  perfect yc?/;'//^  periectjifi/i,  perfect  octave. 


N.  B.     The  peculiar  relations  of  the  fourth  will  be  explained  later,  when  treating  of 
harmony. 

b.   Incomplete. 

The  major  and  minor  third.,  the  major  and  minor  sixth. 


i 


w 


II.     DISSONANCES. 


The  augmented  prime,  the  major,  minor  and  augmented  second, 
the  diminished  third,  the  augmented  and  diminishedyoz/r///,  the  aug- 
mented and  diminishedyf/'//^,  the  augmented  sixth,  the  major,  minor 
and  diminished  seventh,  the  diminished  octave,  and  the  major  and 
minor  ninth. 


Augmented  2.       Diminished  3. 


Augmented.       Diminished  4.    Augmented.    Diminished  5.       Augmented  6. 


Major.        Minor.  Diminished  7.        Diminished  8. Major.  Minor  9. 


MANUAL  OF  HARMONY. 


Inversion  of  Intervals. 


As  has  already  been  shown,  the  interval  is  usually  counted  upward 
from  the  lower  tone.  Should  there  be  reasons,  however,  for  revers- 
ing this  principle  and  counting  downward  from  the  upper  tone,  they 
are  called  intervals  below. 

'^^^"S'  [^^k=f-"=  D  is  the  fifth  above  G.     G  would  also  be  the  fifth 

below  D.      It  will  be  seen  that  the  interval  has  undergone  no  change 
by  this  proceeding. 

It  is,  however,  otherwise,  when  the  upper  tone  of  an  interval  is 
placed  an  octave  lower,  and  consequently  below  the  original  lower 
tone.  If,  for  example,  the  upper  tone  D,  of  the  fifth  G — D,  be  trans- 
posed an  octave  lower,   the  interval  will  change    from  a  fifth    to  a 


fourth ;     thus, 


W^=-p 


This    transposition     of     a  tone    is 


termed  an  inversion  of  the  interval. 

By  means  of  inversion,  the  intervals  of  the  diatonic  major  scale  will 
be  altered  as  follows :  * 


Intervals  Above 

1  2 


8  7 

Intervals  Below. 


The  following:  series  of  numbers  result : 


«         7         b         5         4         3  2  I 

that  is,  through  inversion  the  prime  becomes  an  octave.,  the  second  a 
seventh.)  etc. 

Taking  the  inverted  major  scale  as  a  basis,  we  find — 

1.  All  perfect  intervals  remain  perfect  when  inverted  an  octave. 

2.  All  major  intervals  become  minor,  all  minor,  major,  the  aug- 
mented, diminished,  and  the  diminished,  augmented. 

A  view  of  all  the  inversions  is  shown  in  the  following  table: 


MANUAL  OF  HARMONY. 


19 


Original 
Intervals. 


Inversion, 


Primes. 


^^'s^ 


^^ 


Seconds. 


Perfect.        Augmented. 
Octaves. 


Major. 


Minor. 
Sevenths. 


Augmtnted. 


-¥-_ 


-¥ 


I 


Perfect.        Diminished. 


Major. 


i 


Thirds. 


4= 


--^ 


:epc 


Fourths. 


:»=: 


Major. 


Minor.         Diminished. 
Sixths. 


Perfect,         Augmented.    Diminished. 
Fifths. 


Major. 


_(2_ 


Augmented. 


:#t 


:?N= 


PI 


Diminished.    Augmented. 


Fifths. 


::s: 


-t^ 


.Ji> 


t 


i 


Perfect.  Augmented.      Diminished. 

Fourths. 


Major. 


Minor.  Augmented. 

Thirds. 


m 


'4^- 


m 


SL- 


^ 


-■2— 


tt 


_£2- 


Diminished.      Augmented. 


Major. 


i 


Sevenths. 


:|^ 


Octaves. 


-^- 


Major. 


Minor. 


Diminished. 


i 


42 — ^M— ^ 


Primes. 


Minor.'  Major.'  Augmented.  Perfect.  Augmented. 

An  accurate  knowledge  of  the  inversions  of  intervals  is  not  only 
important  for  the  study  of  double  counterpoint,  but  also  because  it  ren- 
ders the  comprehension  of  the  simple  harmonic  structure  much  easier, 
for  which  reasons  their  study  is  urgently  to  be  recommended. 

A  few  remarks  may  follow  here : 


20  MANUAL  OF  HARMONY. 

The  reason  why.  in  the  first  table  of  intervals  (p.  i6)  all  diminished 
intervals  were  formed  by  raising  the  lower  tone  a  chromatic  half-step, 
and  not  by  lowering  the  upper,  is  easily  to  be  seen  from  the  above 
table  of  inversions.  Since  diminished  intervals  result  from  the  aug- 
mented by  the  inversion  in  the  octave,  this  formation  comes  of  itself. 

For  example,  the  augmented  fourth  '  ^         "^ 


t 


must,  through  inver- 
— .       Also,    the 


sion  produce  the  following  diminished  fifth 

perfect  fourth  belongs  originally  to  the  consonances,  since  it  is 
changed  to  the  perfect  fifth  by  inversion,  just  as  ^^  perfect  fifth  can 
produce  only  the  perfect  fourth.  A  dissonance  can  never  result  from 
the  inversion  in  the  octave  of  a  consonance.  Mention  is  made  here 
of  this  because,  in  special  cases  to  be  noticed  later,  the  fourth  has  to 
be  treated  like  some  of  the  dissonances,  which  in  former  times  led 
some  theorists  to  treat  it  only  as  a  dissonance. 

Likewise  it  will  be  clear  that  the  augmented  octave,  and  also  the 
ninth,  cannot  be  inverted  (in  the  octave),  as  they  can  never  become 
intervals  below. 

Other  kinds  of  inversions,  as  in  the  tenth  and  twelfth,  which  pro- 
duce entirely  different  results,  may  be  passed  over  here,  as  they  have 
no  bearing  on  our  immediate  studies. 

Since  a  complete  and  thorough  knowledge  of  all  the  intervals  is  in- 
dispensable for  the  study  of  harmony,  written  exercises,  as  well  as 
oral  solution  of  given  intervals,  will  greatly  facilitate  their  compre 
hension,  and  should  be  practiced  diligently. 


HARMONY. 


Combinations  of  tones,  sounding  at  the  same  time,  and  composed 
of  different  intervals  according  to  certain  fundamental  principles,  are 
called  in  general,  har7)2onies^  chords. 

The  doctrine  of  harmony  acquaints  us  with  the  different  kinds  of 
chords  and  their  natural  treatment.  This  consists  in  the  correct  and 
nat?iral  co?mecttofi  of  the  chords  with  one  another;  that  is,  in  the 
transition,  resolution,  or  blending  of  one  chord  in  and  with  the 
following. 


PART  I, 


THE  FUNDAMENTAL  HARMONIES  AND  THE  CHORDS 
DERIVED   FROM   THEM. 

Among  the  various  chords  which  may  serve  as  the  harmonic  basis 
of  a  composition,  it  is  easy  to  distinguish  between  those  which  are 
independent,  without  a  definite  connection  with  others,  and  those 
which  require  a  connection  with  preceding  and  succeeding  chords  to 
render  them  intelligible  —  therefore  tiot  independent. 

To  the  first  class  belong  most  of  the  triads,  to  the  second  the 
chords  of  the  seventh.  These  two  varieties  of  chords  form  the 
fu7idamental  hai'tnojties  from  which  all  others  are  derived. 


CHAPTER    I. 

THE   TRIADS    OF    THE    MAJOR    SCALE. 

A  triad  Is  formed  by  a  combination  of  three  different  tones,  hence 
the  name  triad.  The  lowest  of  these  tones  is  called  the  fundamen- 
tal tone,  to  which  are  added  its  third  ^ndffth,  for  example  : 


;b 


22  MANUAL    OF  HARMONY. 

These  triads,  formed  on  C,  G,  and  a,  show  a  difference  in  their 
intervals.  While  the  triads  of  C  and  G  are  formed  of  major  thirds 
and  perfect  Jiftks,  that  of  a  has  a  minor  third  &nd  perfect  Jifth.* 

A  triad  with  a  major  third  and  perfect  fifth  is  termed  a  major 
triad;  a  triad  with  a  ??iinor  third  and  petfect fifth,  a  minor  triad. 

Remark.  —  Triads  of  other  kinds  cannot  be  explained  until  later. 

As  the  diatonic  scale  makes  up  the  essence  of  a  key,  and  forms  the 
groundwork  of  the  melodic  successions,  so  also  the  triads,  which  are 
built  upon  the  different  degrees  of  the  scale,  will  form  the  essential 
part  of  the  harmonic  substance. 

Natural  Connection  of  the  Triads  of  a  Key. 

The  triad  which  is  based  upon  the  first  degree  of  a  key  is  the 
most  important,  since  it  determines  the  key.  There  are,  however, 
others  which  are  nearly  related  and  next  in  importance  to  it,  which 
serve  to  explain  its  position. 

In  the  natural  position  of  the  triad,  third  above  third,  the  lowest 
tone  is  the  fundamental,  \\\q  fifth  the  highest  tone. 


m- 


The  addition  of  any  new  interval  would  either  alter  the  chord  or 
double  some  of  its  tones  already  present. 

The  triad  which  is  nearest  related  to  this  (the  triad  on  the  first  de- 
gree) must,  as  an  independent  chord,  lie  outside  of  it,  yet  rest  upon 
one  of  its  tones.  This  tone  (connecting  link)  can  only  be  found  in 
the  extreme  boundaries  of  the  chord,  namely  C  and  G.  Therefore, 
G,  which  is  the  fifth,  will  form  the  fundamental  of  the  nearest  re- 
lated triad;  while  C  will  serve  a?,  fifth  of  the  other,  the  fundamental 
of  which  will  be  F. 

The  relationship  of  these  three  chords  is  clearly  shown  in  the  fol- 
lowing example  : 


3. 


^ 


F        C  G 

It  will  be  observed  that  these  three  nearly  related  triads  comprise 
all  the  tones  of  the  scale.      They  form  the  foundation  of  the  key  and 


♦Capital  letters  denote  major,  small  letters  minor,  chords. 


MANUAL    OF  HARMONY. 


23 


are,  and  must  be,  more  frequently  employed  in  practical  composition 
than  any  others,  if  the  key  is  to  be  clearly  and  distinctly  presented. 

On  account  of  their  importance,  they  have  received  special  names. 
The  chord  standing  on  the  first  degree  of  the  scale  is  called  the 
tonic  triad;  that  on  the  fifth  degree,  the  dominant  triad;  that  on  the 
fourth  degree,  the  sub-dominant  triad. 

If  w^e  place  these  three  chords  in  their  order  in  the  scale,  without 
showing  their  inner  connection,  they  will  stand  thus: 


* 


I  IV       V 

and  they  are  also  seen  to  be  all  major  triads. 

Application  of  the  Foregoing  Harmonies. 

In  the  application  of  these  three,  as  well  as  other  chords,  we  will 
employ  the  four-voiced  phrase. 

Remark.  —  Theoretical  chord  connection  can,  indeed,  be  illustrated  in  many  ways 
by  the  three-voiced  phrase.  It  would,  however,  keep  us  too  long  from  our  prac- 
tical object,  and  may  be  left  for  special  treatment.  The  four-voiced  movement  will 
always  maintain  its  importance  as  the  basis  of  all  kinds  of  composition. 

We  regard  each  harmony  (chord),  not  as  a  mere  mass,  as  com- 
positions for  the  pianoforte  often  exhibit  them,  but  as  a  combination 
of  tones  to  be  divided  mto  four  different  voices. 

The  upper  part  is  called  the  soprano,  the  lowest  bass.  These  two 
are  called  the  extreme  or  outer  voices.  The  voice  next  under  the 
soprano  is  called  the  alto,  the  one  next  above  the  bass,  tenor.  The 
alto  and  tenor  are  termed  7niddle  voices. 

These  voices  arranged  in  the  manner  of  a  score  will  be  as  follows, 
and  the  triad  appears  thus : 
5. 


Alto. 


i 


S 


i± 


24  MANUAL  OF  HARMONY. 

For  the  three  upper  voices,  or  parts,  different  clefs  are  used,  which 
are  more  suitable  to  their  compass  than  the  violin  (  or  G  clef) . 

These  wall  be  treated  of  hereafter. 

For  the  present  we  will  not  employ  a  separate  stave  for  each  voice, 
but  for  greater  ease  in  reading  the  examples,  we  will  make  use  of 
two,  such  as  are  used  for  piano  music. 

The  distribution  of  voices  in  No.  5,  may  be  shown  thus: 


Soprano. 

Alto. 

Tenor. 


9t 


1^^ 


t 


;i=^i^e=i^i=^=^eb 


In  writing  in  four  parts,  attention  must  be  paid  to  two  things  — 
first,  to  the  progression  of  each  part  for  itself  alofie,  and  then  to  the 
relationship  of  each  part  to  the  three  others,  so  that  both  shall  be  pure 
and  ivell-constructed . 

The  fulfilment  of  these  two  conditions  results  in  what  is  termed 
pure  voice  leading. 

This  purity  of  harmony  and  progression  is  attained  by  seeking  out 
and  practicing  that  which  is  natural  and  laivful  in  the  connection  of 
harmonies.  / 

Thus  arises  the  so-called  pure  part-writing,  or  strict  style,  which 
imposes  rules  and  laws  which  belong  to  the  nature  of  music  itself. 
The  observance  of  these  laws  will  secure  the  surest  foundation  for  a 
free  use  of  the  materials  for  composition.  Exercises  in  pure  part- 
writing  sharpens  the  judgment,  the  sense  of  what  is  true  and  correct 
is  formed,  and  the  taste  cultivated  and  refined. 


Remark.  —  In  so  far  as  every  composition  should  be  the  result  of  a  proper  use  of 
all  available  means  and  the  purity  ( natural  expression  )  obtained  thereby,  the  term 
pure  harmonic  structure,  or  pure  part-writing,  would,  in  a  general  sense  require  no 
further  explanation,  as  being  a  matter  of  course.  In  a  narrower  sense,  however,  by 
pure  harmonic  structure,  something  more  is  understood  which  might  be  better  and 
more  exactly  indicated  by  the  expression  of  similar  meaning,  strict  covipositiou,  strict 
style,  to  distinguish  it  from  free  style,  whereas,  properly  speaking,  nothing  as  op- 
posed to  pure  structure,  as  for  instance,  impure  structure,  is  to  be  assumed ;  since, 
however  often  it  may  occur,  is  always  to  be  designated  as  false,  while  the  free 
structure  could  be  based  upon  what  is  legitimate  in  the  pure  style. 

As  was  said  before,  by  pure  harmonic  structure,  in  the  narrower  sense,  is  under- 
stood such  a  one  as  in  the  natural  development  of  tone  relations,  allows  the  fewest 


MANUAL  OF  HARMONY. 


25 


deviations  from  what  is  legitimate,  and  only  such  as  do  not  trench  upon  that  which 
is  essential  or  fundamental. 

If  the  idea  of  pure  harmonic  structure  is  thus  determined  in  a  general  way,  still  its 
limits  are  not  yet  drawn  ;  and  it  is  just  this  point  which  creates  all  the  more  difficul- 
ties for  the  beginner,  since  the  limits  are  so  variously  fixed  by  theorists  themselves. 
This  difficulty  has  caused  many  of  them,  especially  some  of  the  more  modern  ones,  to 
say  nothing  of  pure  construction,  or  strict  style,  but  to  begin  at  once  with  compo- 
sition, and  teach  the  laws  of  harmony  incidentally.  Whether  this  indulgence  with 
youthful  impatience  which  does  not  like  to  busy  itself  with  the  abstract  —  this  ten- 
dency towards  premature  living  creation  before  the  organic  has  developed  into  a 
creative  capability,  can  produce  anything  really  mature,  will  not  be  further  investigated 
here. 

Those  who  follow  the  views  of  this  book  and  conform  their  studies  to  them,  as 
well  as  those  who  have  to  go  through  a  strict  school,  may  be  assured  that  their  free- 
dom for  future  creation  will  by  no  means  be  lost  by  means  of  that  which  is  forbidden 
them,  but  will  develop  itself  more  fully  and  with  more  vital  power  upon  a  basis  con- 
formable to  nature.  Real  mastery  has  ever  learned  to  make  itself  felt  most  genially  with- 
in certain  limits,  whereas  the  most  fantastic  ideas  often  furnish  proof  of  a  weak  and 
morbid  mind.  On  the  other  hand  the  student  will  not  be  justified,  where  rules  are 
concerned,  in  making  use  of  exceptions  to  those  rules  which,  perhaps,  may  be  found 
in  the  works  of  the  best  masters,  or  in  general,  in  wishing  to  produce  composition, 
when  the  proper  thing  is  to  work  exercises  theoretically  well. 

The  employment  of  the  three  chords  already  found,  when  applied 
in  four-part  harmony,  will  afford  opportunity  for  remarks  and  obser- 
vations, and  necessitate  certain  rules  and  fundamental  principles. 

As  the  triad  is  composed  of  only  three  tones,  one  of  its  intervals 
must  be  doubled  when  four  parts  (voices)  are  to  be  used. 

Any  interval  of  the  triad  may  be  doubled^  but  the  fundamental 
is  the  one  best  adapted  for  this  purpose,  more  seldom  the  fifth  and 
third,  while  there  are  cases  in  which  the  third  is  not  to  be  doubled  at 
all. 

To  accomplish  the  connection  of  two  triads,  one  with  another,  the 
following  rule  must  be  observed : 

When  any  one  tone  occurs  in  two  chords  which  are  to  be  connected, 
it  is  to  be  retained  in  the  same  voice,  e.  g. 


^ 


I 


26 


MANUAL  OF  HARMONY. 


In  the  example  a,  C  is  a  tone  found  in  both  chords.  The  soprano, 
which  had  the  C  in  the  first  chord,  retains  it  also  as  the  fifth  of  the 
next  chord.  Likewise  in  example  (5,  the  alto  makes  the  connection 
by  taking  G  in  both  chords. 

The  remaining  voices  proceed  to  those  tones  of  the  following  chord 
w^hich  lie  ?iearest  to  thetn^  as  in  example  a,  the  alto  from  G  to  A, 
and  the  tenor  from  E  to  F,  etc. 

When  two  consecutive  chords  are  composed  of  entirely  different 
notes,  the  voices  are  led  in  such  a  manner  as  to  avoid  what  are  termed 
parallel  fifths  and  octaves. 

In  order  to  explain  this  objectionable  progression  more  fully,  we 
must  first  consider  the  relation  of  one  part  to  another  as  regards  the 
movement  of  the  voices. 


The  Movement  of  Voices  in  respect  to  each  other. 

One  voice  can  progress  with  another  in 

Parallel  [direct]  motion  {inohis  rectzis), 
Contrary  motion,  {inotus  contrarius)  and 

Oblique  motion,  {motus  obliquus)  . 

Parallel  motion  occurs  if  two  voices  rise  or  fall  at  the  same  time, 


$ 


z^t. 


^^^glH 


Thev  move  in  contrary  motion  if  the  one  rises  and  the  other  falls, 
e.  (T. 


% 


I  [-  -^-  '  I  1  I    . 

Oblique  motion  occurs  when  one  voice  remains  on  the  same  tone 
while  the  other  ascends  or  descends,  e.  g. 


1  o.  trfcz:^ 


?^ 


g 


I 


MANUAL  OF  HARMONY.  27 

A  mixture  of  tliese  three  kinds  of  motion  occur  in  ciiord  connections. 
Tlius,  in  No.  7,  at  <5,  the  soprano  and  tenor  move  in  parallel  motion, 
while  contrary  motion  is  found  between  soprano,  tenor  and  bass,  and 
oblique  motion  between  the  alto  and  all  the  other  voices. 

The  above-mentioned  faulty  progression  in  parallel  octaves  and 
Jift/is,  can  only  occur  in  parallel  motion,  if  for  example,  two  voices 
move  by  degrees  or  skips  from  a  perfect  fifth  or  octave,  to  another 
perfect  fifth  or  octave,  thus : 

Parallel  octaves  Parallel  fifths  Parallel  octaves  Parallel  fifths 

by  degrees.  by  degrees.  by  skips.  by  skips. 


^^^^- 


These  movements  are  regarded  i\.?,  faulty  for  all  voices. 
The  following  progressions  of  harmony  contain  both  faults : 


,..! 


n^^^m-_ 


W^eMi 


'-^ 


The  faulty  parallels  are  indicated  by  the  oblique  lines. 

In  example  a,  there  are  jDarallel  octaves,  by  skips,  between  soprano 
and  bass,  and  parallel  fifths  between  alto  and  bass.  In  example  6^ 
parallel  octaves,  by  degrees,  are  found  between  alto  and  bass,  and 
fifths  between  tenor  and  bass,  and  in  example  c,  octaves,  by  degrees, 
between  tenor  and  bass,  and  fifths  between  soprano  and  tenor,  and 
soprano  and  bass. 

To  avoid  these  and  similiar  faulty  movements  of  the  voices,  it  is 
necessary  that  the  voices,  between  which  the  fault  lies,  should  be  led 
in  contrary  or  oblique  motion  with  each  other ;  that  is,  the  voice  which 
forms  an  octave  or  fifth  with  another,  must  move  in  contrary  motion 
with  it,  or  in  case  the  next  chord  contains  the  same  to?ze,  fnust  remain 
stationary.,  thus  producing  oblique  motion.  The  remaining  voices 
then  move  to  the  nearest  intervals  of  the  new  harmony. 

Thus,  in  example  I3,  a.,  one  voice  must  remain  on  C,  while  the 
others  pass  upward,  resulting  in  oblique  motion  between  the  alto  and 
all  the  otlier  parts.      At  b  and  c,  contrary  motion   to  the   bass  must 


28 


MANUAL  OF  HARMONY. 


be   used   in  all  the  parts — at  b,  toward  the  bass,  at  r,  fro??i    it,  for 
example  : 


Remark.  — The  reason  for  x)\&  prohibition  of  octaves  (also  the  unison)  can  be  eas- 
ily found  in  the  necessary  independence  of  the  parts.  The  reason  for  the  prohibition 
of  Ji/th  progressions  is  more  difficult  to  discover,  however  much  we  may  feel  the 
necessity  of  it ;  and  from  the  earliest  times,  much  pains  have  been  taken  to  express  it 
clearly  and  definitely.  Let  the  following  view  on  this  point  be  examined.  If  each 
chord-formation  presents  for  itself  a  distinct  whoie,  which,  however  else  it  may  be 
formed,  yet,  in  respect  to  its  fundamental  and  fifth  mainly,  unites  itself  as  it  were  into 
z.  circle  (the  seventh,  as  an  addition,  not  being  considered  here),  and  if  connections 
of  harmony  can  only  be  produced  by  one  chord,  so  to  speak,  going  over  and  passing, 
or  resolvmg  into  another,  then  it  is  plain  that  two  chords  having  their  extremes  fifth 
following  fifth,  cannot  resolve  themselves  into  each  other,  but,  when  placed  side  by 
side,  will  appear  without  any  relation  to  each  other. 

This  can  be  seen  by  comparing  the  following: 


14-, 


a. ^ 


The  sevenths  do  not  form  essentially  new  chords,  neither  do  they  lie  beyond  the 
circle  of  the  primary  chord:  they  only  serve  to  indicate  more  distinctly  the  relation- 
ship of  two  chords,  and  make  the  connections  more  intimate  and  firm. 

Now,  wherever  the  pe7'fect  fifth  appears,  it  will  carry  in  itself  the  character  of  bound- 
ary; and  whether  the  remaining  parts  of  the  chord  (the  contents  as  it  were  of  the 
fifth)  or  an  added  interval  like  the  seventh,  lie  above  or  below  it,  the  disagreeable 
effect  of  tivo  perfect  fifths  in  succession  will  always  be  found  to  consist  in  the  lack 
of  connection. 

While  speaking  here  of  the  fifths  of  triads  only,  it  may  still  be  observed,  that  in  the 
case  oi  perfect  fifths  which  arise  from  added  sevenths,  the  requirement  of  their  prepa- 
ration, partly  of  itself,  prevents  parallel  fifths ;  but  in  the  case  of  the  progression  of 
such  a  seventh  which  forms  a  perfect  fifth  with  another  voice,  to  another  perfect  fifth, 
the  unpleasantness  and  lack  of  connection  will  be  preceptible  in  the  second'^i'Cn.  only 
which  enters  without  connection,  e.  g. 


i 


"m 


MANUAL  OF  HARMONY. 


29 


Concerning  the  diminished  fifth,  however,  which  in  the  dominant  seventh  chord 
can  enter  free  (unprepared)  in  certain  cases,  its  entrance  unprepared,  even  in  the  case 
of  parallels,  perfectly  justifies  the  views  expressed  above,  for  whenever  \\.  follows  the 
perfect  fifth,  its  connecting  character  is  felt,  but  when  \i  precedes  it,  the  latter,  taking 
no  account  of  the  laws  of  progression,  steps  at  once  outside  of  the  connecting  circle  of 
both  harmonies.     Compare  the  following: 

a.        ,  b.  c. 

4=^^ 


ji^ 


t^=F 


-^ 


^ 


fe 


_g. 


If  passages  like  the  following  are  frequently  found  in  compositions  of  the  stricter 
fltyle : 


1^ 


iPB 


it  may  be  assumed  that  the  doubling  of  the  diminished  fifth  (the  F)  requires  a  double 
progression  of  the  same,  and  that  the  succession  of  fifths  are  justified  because  they 
lie  in  the  middle  voices,  but  that  the  following  progressions  could  not  be  called  pure, 


J 


i=^ 


J 


9t 


^=^~ 


partly  because  they  are  too  prominent  in  the  upper  voice;  partly  because  the  above 
condition  of  a  necessary  double  progression  is  wanting,  although  passages  like  No. 
16,  c,  are  plentiful  enough. 

Here  it  also  becomes  clear  why  such  parallel  fifths  as  arise  through  passing  notes, 
in  many  cases  do  not  sound  as  disagreeably  as  those  mentioned  above,  and  for  this 
reason  many  theorists  regard  them  as  faultless.  This,  however,  cannot  be  admitted 
altogether,  since  many  of  them  are  based  upon  other  false  progressions  (for  exam- 
ple, upon  covered  fifths),  and  it  is  not  to  be  denied,  that  with  a  very  open  position 
and  a  sufficiently  long  duration,  their  unpleasant  effect  is  noticable. 


30 


MANUAL  OF  HARMONY. 


It  is  not  the  place  here  to  treat  further  of  these  relations,  and  there  would  be  much 
to  say  on  many  points,  as  for  example,  the  progression  of  the  fifth  in  the  augmented 
chord  of  the  sixth  and  fifth,  but  which  would  lead  us  too  far.  Individual  cases  will 
lead  us  back  to  this  point  in  connection  with  our  practical  exercises.  If  the  meaning 
of  the  foregoing  remarks  be  too  obscure  for  the  beginner,  with  more  advanced  knowl- 
edge and  practice  in  the  entire  harmonic  system,  it  will  soon  be  comprehended. 

The  faulty  progression,  thus  far  mentioned,  is  called  Open  fifth  and 
octave  progression. 

They  are  called  covered  if,  in  parallel  motion  of  two  voices,  the 
second  interval  forms  a  fifth  or  octave,  e.  g. 


19. 


Open  parallel  fifths  and  octaves  for  harmonic  connections  are  never 
admissable ;  the  worth  of  covered  fifths  and  octaves  will  be  discussed 
later  (Chap.  XVII.)  ;  for  the  present  this  must  be  left  for  oral  instruc- 
tion, as,  in  general,  with  a  correct  understanding  of  the  exercises, 
there  will  be,  at  present,  little  opportunity  for  errors  in  making 
objectionable  fifths  and  octaves. 

Remark.  —  The  beginner  will  do  well,  when  working  out  his  first  exercises,  to  pay 
no  attention  to  covered  fifths  and  octaves,  because,  in  his  anxiety  to  avoid  them,  th* 
first  principles  of  chord  connection  are  violated,  and  worse  faults  may  easily  arise. 

Exercises. 

The  n6xt  exercise  will  be  to  employ  the  three  primary  triads  in  con- 
nection with  each  other,  musically  and  with  observance  of  the  rules 
thus  far  established. 

For  this  purpose  we  select  the  following  bass  progression : 


iili* 


C:  I 


I      IV 


t 


& 


s^:: 


lis^il^ 


I 


*When  a  figure  appears  over  the^rj/ bass  note  the  soprano  should  take  the  interval  indicated; 
thus,  3  indicates  the  third  of  the  chord,  s,  the  fifth,  etc. 


MANUAL    OF  HARMONY. 


31 


Remark. — These,  and  all  following  exercises,  indicate  the  way  and  method  in  which 
our  exercises  will  proceed.  They  should  be  continued  as  long  as  the  subject  in  hand 
requires  it. 

The  disposal  of  the  three  upper  voices  of  the  first  chord,  wliich  are 
to  be  added,  will  give  occasion  for  important  remarks.  We  have 
already  seen  in  example  5,  that  the  situation  of  the  voices  in  a  chord 
may  vary  greatly.  This  situation  of  the  voices  is  called  the  position 
of  the  chord. 

Close  and  Open  Position. 

A  chord  is  said  to  be  in  close  position,  when  the  upper  voices  lie 
so  near  each  other  that  neither  the  soprano  nor  tenor,  if  transposed  an 
octave,  would  fall  between  the  other  two  voices,  the  bass  being  more 
or  less  distant,  e.  g. 


)i 


d. 


;r^ig^l=i 


^=g: 


il^^E^H 


91: 


The  first  position  of  the  chord,  «,  is  so  changed  in  /^,  that  the  former 
E  of  the  tenor  is  placed  an  octave  higher  in  the  soprano ;  in  c,  the 
case  is  the  same  with  both  tones  G  and  E ;  in  fl^,  the  C  of  the  soprano 
is  placed  an  octave  lower  and  becomes  the  tenor.  In  all  these  trans- 
positions the  distribution  is  altered,  but  the  close  positiott  is  still 
retained. 

It  is  otherwise  when  the  chord  appears  in  open  position  (also  called 
dispersed,  sometimes  extended  position),  which  is  the  case  if  either 
the  soprano  can  be  placed  between  the  alto  and  tenor,  or  the  tenor  be- 
tween the  alto  and  soprano,  so  that  the  result  will  be  close,  e.  g. 


t 


i^r^g^sisgSBrii 


/ 


9t 


-o'- 


32 


MANUAL    OF  HARMONY. 


At  a,  the  chord  appears  in  open  position ;  by  transposing  the  G  an 
octave  higher  (between  alto  and  soprano),  in  close  position,  as  at  (5; 
the  same  at  c  and  d.  At/,  the  G  of  the  soprano  of  the  chord  at  e  is 
placed  an  octave  lower  and  between  alto  and  tenor. 

The  following  situation  of  the  voices,  a,  (No.  23)  would  not,  how- 
ever, be  an  open  position  in  this  sense,  for  by  transposing  the  tenor, 
the  situation  of  the  upper  voices  would  not  be  changed,  b^  and  only 
the  transposition  of  the  soprano  would  give  the  chord  in  the  real  opea 
position,  as  at  c. 


23. 


I 


ll^l^] 


The  open  position,  although  it  makes  the  chord  appear  fuller,  is  not 
always  to  be  used,  not  being  clear  enough  to  the  view ;  therefore,  for 
the  present,  the  exercises  will  be  written  in  close  position. 

Remark. —  It  will  always  be  better,  at  first,  to  write  the  examples  in  close  position, 
and  only  use  the  open  position  later,  from  the  exercises  in  the  second  and  third  part, 
where  it  will  be  found  necessary.  By  using  the  open  position  in  the  beginning,  the 
pupil  stumbles  upon  difficulties  which  is  not  to  our  immediate  purpose  to  surmount, 
and  which  may,  therefore,  be  better  to  avoid. 

The  different  positions  do  not  usually  appear  singly,  but  occur  to- 
gether,  as  the  leading  of  the  voices  requires. 

The  position  of  the  jfr^/  chord  having  been  decided,  the  chords  fol- 
lowing are  no  longer  so  free  that  their  positions  may  be  chosen  at  will, 
but  must  be  governed  by  the  rules  already  given  for  the  connection 
of  chords.      (Pages  25  and  26.) 

The  connection  of  chords  and  leading  of  voices  in  the  first  exercise. 
No.  20,  may  be  as  follows : 


^^gi^i^^^H 


9t 


I 


C:     I 


IV 


MANUAL   OF  HARMONY. 


33 


The  natural  relationship  of  these  chords  to  one  another  can  be 
clearly  seen  bv  observing  the  connections.  But  especially  from  the 
last  two  chords  does  the  close  connection  show  how  one  completes 
the  other.  From  the  feeling  of  rest  and  satisfaction  induced  by  the 
concluding  progression  in  the  above  example,  it  has  been  named  the 
authentic  close  or  cadence. 


Another  form  of  close,  or  cadence,  is  formed  through  the  sub- 
dominant  triad,  as  in  No.  20,  fourth  example,  and  is  called  the 
plagal  close  or  cadence. 


N,  B.  The  last  chord  of  a  cadence  (close)  always  falls  on  the  accented  part  o! 
the  measure.  —  PZd. 

Of  these  and  other  kinds  of  close,  we  cannot  speak  at  length  until 
later. 

In  order  to  become  accustomed  to  the  succession  of  chords  which 
occurs  when  the  bass  progresses  by  degrees  (as  in  Ex.  34,  F — G), 
it  w^ould  be  advisable  to  write  out  the  progressions  IV — V  and  V — IV, 
in  various  positions  and  keys. 

The  Triads  of  the  Remaining  Degrees  of  the  Major  Scale. 

All  the  triads  situated  on  the  remaining  degrees  of  the  major  scale, 
although  they  certainly  belong  to  that  scale,  do  not  indicate  it  so 
plainly  as,  for  instance,  the  chord  connection  V — I. 

These  triads  are  called,  to  distinguish  them  from  the  primary  triads, 
secondary  triads. 


34 


MANUAL    OF  HARMONY. 
SECONDARY   TRIADS. 


They  are  situated  upon  the  second,  third,  sixth  and  seventh  degrees 
of  the  scale. 


27 


•a^ii 


^=i 


-G—^ 


«  ^ 


The  triads  of  the  second,  third  and  sixth  degrees  are  minor  triads, 
as  their  thirds  are  minor  and  their  fifths  perfect. 

The  triad  of  the  seventh  degree  differs  from  all  the  others,  since, 
beside  the  minor  third,  it  has  a  diminished  fifth ;  hence,  it  is  called 
the  diminished  triad. 

In  order  to  distinguish  between  major  and  minor  triads  in  the  sys- 
tem of  Roman  numerals  under  the  bass  notes,  we  will  employ  a  large 
numeral  for  the  major,  a  small  one  for  the  minor,  and  for  the  dimin- 
ished triad  we  add  a  °,  as  above,  vii°,  a  method  introduced  by  the 
theorist,  G.  Weber. 

All  the  triads  of  the  major  scale  will  now  stand  thus : 


28. 


Remark.  — The  beginner  must  beware  of  mistaking  any  of  these  chords  for  tonic 
triads,  an  error  which  malics  an  insight  of  harmonic  relations  much  more  difficult. 

As  long  as  the  key  remains  in  C  major,  as  in  the  above  example,  the  various  chords 
of  F,  G,  D,  andC,  are  merely  chords  of  the  different  degrees  of  C  major,  and  cannot 
belong  to  the  key  of  F,  or  G,  unless  such  keys  are  reached  by  and  through  tnoJulatioti. 

Hereby  arises  an  ambiguity  of  the  chords  which  should  be  carefully  noticed. 
Each  triad  can  belong  to  different  keys.  Thus,  in  the  following  example,  the  major 
triad  of  C  can  be  : 


29. 


i 


C:  I 


7^ 


I 


If,  therefore,  with  respect  to  this  chord,  C  major  is  spoken  of  (meaning  the  key, 
according  to  ordinary  usage  )  this  would  be  true  only  in  the  first  case  where  the  C 
major  triad  stands  on  \.)\&Jirst  degree,  but  in  all  other  cases  is  incorrect. 


MANUAL  OF  HARMONY. 


35 


Application. 

No  new  rules  are  required,  at  25resent,  for  the  connection  ot  tiie 
secondary  chords  with  each  other,  or  with  the  three  primary  triads. 
Several  new  features  will  appear,  however,  in  this  connection. 

The  bass  can  move  either  by  skips  or  by  degrees.  In  the  former 
case  there  will  always  Idc  a  connecting  tone,  a  tone  common  to  two 
consecutive  chords,  and  this  tone  should  be  allowed  to  remain  in  the 
same  voice^  as  shown  in  Ex.  24.  In  the  latter  case  there  will  be  no 
connecting  tone,  and  the  voices  must  be  led  in  contrary  tnotion  with 
the  bass,  in  order  to  establish  the  inner  connection  of  the  chords. 


a.     The  Bass  moves  by  Skips. 
b.  N.B.        better. 


SO. 


^Eia; 


n^ir^a^iTr^ii^^ 


iSil^igilg^igia 


II     IV  II      V  II      VI 

In  the  above  example,  the  bass  proceeds  by  skips  of  various  degrees, 
tile  upper  parts  being  connected  by  tones  common  to  both  chords,  and 
iv/iick  remain  in  the  same  voice.  There  are  exceptions  in  many 
cases,  however,  to  this  rule. 

In  Ex.  30,  at  N.  B.,  is  a  progression  of  the  voices  formed  accord- 
ing to  this  rule,  where  are  found  covered  octaves  between  the  tenor 
and  bass,  which  it  would  be  better  to  avoid  by  means  of  the  progres- 
sion which  follows.  Though  the  local  connection  would  thus  be 
lacking,  still,  the  /V?«<?r  connection  is  present,  as  the  D  of  the  soprano 
in  the  Jirst  chord  can  easily  be  imagined  as  being  doubled  in  the  lower 
octave,  when  the  connection  at  once  becomes  plain,  as  in  Ex.  31  : 


Remark.  —  The  reason  why  just  t/n's  tone  should  be  imagined  as  being  doubled, 
since  that  might  be  the  case  with  any  other,  is  based  upon  the  fact  that  it  is  the/unda- 
mental — the  tone  which  determines  the  whole  character  of  the  chord. 


36 


MANUAL  OF  HARMONY. 


The  reason  why  such  covered  octaves  are  unpleasant  is  because  the 
upper  voice  proceeds  a  -whole  step^  and  is  more  noticeable  still  it 
contained  in  an  outer  voice,  as  in  Ex.  33,  at  a. 


Contrary  motion  of  the  bass,  as  at  <5,  would  improve  the  progression, 
also,  by  contrary  motion,  as  at  c,  although  here  a  covered  fifth 
show^s  itself  betv^^een  the  soprano  and  tenor.  (See  the  Remarks  on 
Ex.  34.) 

Remark.— In  the  cases  given  above,  we  do  not  speak  of  absolute  faults.  If  we 
are  given  entire  control  of  all  the  parts,  much  can  be  avoided  which  under  other  cir- 
cumstances, for  instance,  in  treating  a  cantiis  firmus,  or  a  motive,  or  for  other  reasons 
regarding  the  composition,  is  impossible.  The  improvement  is  here  only  given  from 
a  theoretical  stand-point.  Regarding  the  covered  fifth  in  No.  32,  c,  further  remarks 
follow  under  No.  34. 

Covered  octaves  cease  to  have  any  unpleasant  effect  when  the 
upper  voice  proceeds  by  a  half  step,  e.  g. 


t 


-tf^— I — ^' 


^E^^^ 


^^ 


b.     The  Bass  moves  by  Degrees. 
Here  contrary  motion  will  always  be  employed,  e.  g. 
better. 


34. 


MANUAL  OF  HARMONY. 


37 


I 


better. 


jjElEl^l^^^ 


9t 


^:=^=^ 


:l^^ 


N.R.     2. 


^ 


IV 


In  all  progressions  like  that  at  N.  B.  i  (I— II),  and  subsequent  like 
places,  it  is  better  to  double  the  third  in  the  second  chord,  in  order  to 
avoid  the  covered  fifths  between  soprano  and  tenor.  Their  unpleasant 
effect  is  still  more  preceptible  when  the  chords  are  in  open  position  : — 


^ 

a.                                                       b. 

_^^_L 1__^_^« j 

1-^- 

~-^ — ^^F 

St 

^-^^TS ' ^ ' & 

-    <?     —& ^ ^ — a 

l^S-\-^ 2^T=^ 

-<S2- 

The  progression  at  b  is  preferable.  If,  however,  the  covered  fifths 
are  between  the  middle  voices,  they  are  not  so  perceptible,  and  there- 
fore less  objectionable : 


36. 


i^^ 


9t 


At  N.  B.  2,  the  doubling  of  the  third  in  the  second  chord  is  not 
always  feasible,  because  the  doubling  of  the  seventh  degree  (in  Ex. 
34,  the  B  of  the  second  chord)  is  usually  to  be  avoided. 

The  treatment  of  this  tone,  which  is  called  the  leading  tone,  will  be 
further  discussed  in  connection  with  the  exercises  which  follow. 


38 


MANUAL  OF  HARMONY, 

Exercises  to  be  worked  out. 


^ 


•  ii^^pg^^^g;ii^^^ 


^^^liii^e^i^PS^ 


25) — &- 


^^ 


N.  B. 


WF=t= 


:F==tt: 


■^=F 


:5=^ 


^iii 


P=F 


-^-^- 


*     t 


:9^ 


^:^^'^-X'\f'^^^^mm^f^^ 


II    V      VI 


ag^^^^p^^gs 


m 


10.      ^  **  11-  5 


i5^; 


-«> f=2_ 


:z^ 


III     IV 


giiEiBiPii&'^ 


:2-=^ 


13.  5 


as 


;=F=* 


E3E^: 


:| ^: 


i 


I      II 

The  fourth  of  the  above  exercises  gives  occasion  for  some  remarks. 
It  will  be  observed  that  the  movement  of  the  bass  in  the  first  measure 
is  repeated  in  the  three  vv^hich  follow.     Any  such  regular  harmonic  or 


See  Ex.  30.    t  See  Ex.  42.    *•  See  Ex.  34.    $  See  Ex.  34. 


MANUAL  OF  HARMONY. 


39 


melodic  progression  is  called  a  sequence,  and  demands  a  correspond- 
ing regularity  in  the  other  voices.  This  regularity  could  not  be  ob- 
tained by  working  exactly  according  to  the  rules  already  given,  thus : 


i 


^ 


m 


r-r^ 


-6^ 

etc. 


t 


^i 


It  will  therefore  be  necessary  to  lead  the  soprano  by  a  skip  at  the 
end  of  the  first  measure,  in  order  to  bring  the  Jirst  chord  in  each 
Tncasta-e  into  the  same  position,  and  thus  preserve  the  uniformity  of 
the  sequence.      The  following  will  make  it  plain. 


39. 


^ 


J V 


N. 


l^a-Fg=g 


1 


§±ffiE3^ 


IV         II      VI      III     viio 

In  the  first  example,  the  covered  octaves  are  tolerated  on  account 
of  the  sequence,  but  they  cannot  be  allowed  in  the  outer  voices.  The 
first  exercise  in  No.  37  can  also  be  worked  as  a  sequence. 

In  the  third  measure  of  Ex.  4,  we  find  a  chord  which  we  have  not 
yet  used,  called  the  diminished  triad.  This  chord  rests  upon  the 
seventh  degree  of  the  major  scale,  and  is  not  as  independent  as  those 
on  the  other  degrees,  since  its  diminished  fifth,  which  is  a  dissonance, 
plainly  indicates  a  progression.  The  natural  progression  of  dimin- 
ished intervals  is,  in  general,  that  both  tones  approach  each  other  by 
a  degree  (a),  or  that  one  moves  while  the  other  remains  stationary 
(<5,  c),  a  sort  of  progression  which  only  becomes  plain  by  actual 
chord-connection. 


e.     Inversion. 


^^i^^^^i^l^ 


In  the  third  which  follows  the  diminished  fifth  (triad),  the  triad  on 


40  MANUAL  OF  HARMONY. 

the  first  degree  (c)  will  appear  in  an  incomplete  form— without  its 
fifth,  as  at  d. 

Since,  according  to  the  relations  of  intervals  in  regard  to  inversion 
(which  has  been  explained  under  "intervals"),  an  augmented  fourth 
results  from  the  diminished  fifth,  its  progression  will  also  take  place 
in  an  inverted  manner.      (See  40,  e.) 

N.  B.  It  should  be  noticed  that  the  fundamental  rises  and  the  fifth /rZ/j-  in  the  in- 
version, just  the  same  as  in  the  fundamental  position  of  the  chord.  The  tendency  of 
the  half-steps  to  proceed  to  the  nearest  tones  is  thus  shown. — Ed. 

The  fundamental  tone,  upon  which  the  diminished  triad  is  formed, 
is  called  the  leading  tone. 

It  senses  as  third  in  the  dominant  triad,  and  Sisjifth  in  the  triad  on 
the  third  degree. 


41. 


^=^ijS=^Jtz:H 


As  the  leading-  tone.,  of  itself,  is  heard  very  distinctly,  it  is  7iot 
doubled  in  simple  four-part  harmony.  Also,  its  progression  should  be 
upward  a  half-step  to  the  tonic,  providing  that  tone  is  contained  in 
the  next  chord. 

This  tendency  to  an  upward  progression  lies  in  the  melodic  char- 
acter of  the  leading  tone,  as  it  stands  but  a  half-step  below  the  tonic 
of  the  scale.  This  is  particularly  observable  in  the  dominant  triad, 
when  the  leading  tone  appears  in  the  highest  voice,  as  Ex.  42,  a,  is 
more  satisfying  than  b  or  c. 


When  appearing  in  a  middle  voice  the  upward  tendency  is  not  so  de- 
cided, as  at  d.  Skips  from  the  leading  tone  downward,  when  taken 
by  the  upper  voice  (c)  are  intolerable,  but  when  in  a  middle  voice 
can  be  taken  if  the  bass  moves  in  contrary  motion,  as  at  c. 


MANUAL  OF  HARMONY. 


41 


In  Ex.  39,  in  the  third  measure,  at  N.  B.,  the  leading  tone  is  found 
doubled  and  progressing  contrary  to  the  above  rule.  Both  were  the 
result  of  the  sequence  contained  in  the  example,  which  would  not  admit 
of  change  in  the  position  or  progression  of  the  chords. 

On  the  More  Complete  Formation  of  the  Close. 

The  close  by  means  of  the  dominant  chord  (authentic  close), 
appears  in  a  still  more  definite  form  in  the  last  examples.  For,  while 
the  natural  i-elationship  of  the  dominant  triad  to  that  of  the  tonic  makes 
these  two  chords  the  most  suitable  for  the  formation  of  the  close,  in 
the  first  and  second  exercises  of  Ex.  37  may  be  observed  a  prepara- 
tion of  a  close  by  means  of  the  triad  on  the  second  degree.,  which 
bears  the  same  relation  to  the  chord  of  the  dominant  as  this  latter  does 
to  the  tonic  triad,  e.  g. 


t 


g^i; 


Instead  of  the  triad  on  the  second  degree,  the  subdominant  can  also 
be  used  to  prepare  the  authentic  close,  e.  g. 


iES 


IV 


;h 


The  forms  of  closing  resulting  from  this  connection  of  chords,  will 
assume  a  more  definite  form  by  the  use  of  chords  to  be  explained 
hereafter. 


.2  MANUAL    OF  HARMONY. 


CHAPTER   II. 

THE    TRIADS    OF    THE    MINOR    SCALE. 

a.     Primary  Triads. 

The  primary  triads  of  the  major  scale  were  found  on  the  Jirst., 
foiirth.,  Sim\Jifth  degrees.  Those  of  the  minor  scale  are  found  on  the 
same  degrees. 

The  pecuUar  j^«a/  feeUng  induced  by  the  authentic  close,  is  caused 
by  the  fact  that  the  last  chord  but  one  contains  the  seventh  degree  of 
the  scale,  or  leading  tone,  and  that  this  tone  is  only  a  half-step  distant 
from  the  tonic,  or  key-note.  For  if  the  seventh  degree  were  distant 
from  the  tonic  a  -whole  step,  which  according  to  the  signature  of  the 
minor  scale  is  the  case,  it  would  not  possess  the  characteristics  of  the 
leading  tone.  Therefore,  to  make  the  authentic  close  in  the  minor 
key,  it  is  necessary  lo  raise  the  seventh  degree  chromatically  a  half- 
step,  by  which  means  it  acquires  the  character  of  the  leading  tone,  e.  g. 


45. 


i 


i 


-7S—S>- 


sr-^- 


N.B. 


In  consequence  of  this  alteration  the  dominant  triad  is  precisely  the 
same  in  major  or  minor,  or  in  other  words,  the  dominant  is  al-ways  a 
major  triad. 

A  major. 


ma 


*       a: V  A:Y 

This  will  be  clearly  shown  by  comparing  the  close  in  both  keys ; 


•  In  the  indications  below  the  staff,  observe,  that  a  large  letter  indicates  a  major  key,  a  small 
letter  a  minor  key,  a  large  Roman  numeral  a  major  triad,  a  small  numeral  a  minor  triad, 
etc.— Eu. 


MANUAL    OF  HARMONY. 


43 


^ 


C  major.  C  minor. 

fipiiiiipni"] 
11 


As  a  proof,  however,  that  a  similar  alteration  of  the  sixth  degree  is 
not  allowable  in  harmony,  though  continually  adopted  in  melody,  it 
is  only  necessary  to  examine  the  plagal  close,  shown  at  a  in  the  fol- 
lowing example,  which,  it  will  readily  be  seen,  could  not  possibly  be 
conceived  of,  as  at  b. 


H 


Si: 


-^-■- 


-^ 


1 


The  three  primary  triads  of  the  minor  scale  and  their  relationship, 
may  be  shown  thus  : 


.  ^i==S=fe| 


IV        I        V 

The  minor  scale,  as  a  basis  for  the  harmonic  structure,  will  there- 
fore stand  thus : 


^^•"P^—^ ^^ 


t 


Remark. — All  other  forms  of  the  minor  scale,  as  : 


i 


^       <^ 


j^fc 


;i 


44 

or  descending: 


MANUAL  OF  HARMONY. 


52. 


* 


-^ ^ 


rest  upon  melodic  conditions  which  prohibit  the  step  of  an  augmented  sc-ond  between 
the  sixth  and  seventh  degrees,  as  seen  in  No.  50.  In  the  abstract,  these  forms  have 
no  influence  on  the  harmonic  structure ;  still  the  harmonic  foundation  reacts  on  the 
minor  scale  itself,  as  the  following  examples  show  : 


H: 


m- 


Wz 


The  last  case,  in  which  the  descending  scale  makes  the  step  of  an  augmented  second, 
B — Ab,  and  which  we  shall  carefully  avoid  in  future  chord-connections,  is  to  be  explained 
in  this  way — that  the  B  was  necessary  as  a  component  part  of  the  chord  (the  third  in 
the  dominant),  but  the  Aft,  however,  was  needed  so  as  not  to  destroy  the  minor  charac- 
ter of  the  passage  which  would  have  been  the  case  very  perceptibly  by  Aj,  while  in  the 
ascending  scale  (in  the  first  example)  this  minor  character  is  already  well  preserved 
by  the  minor  third,  d?. 

b.     The  Triads  of  the  Other  Degrees  of  the  Minor  Scale. 

SECONDARY   TRIADS. 
According  to  the  establishment  of  the  minor  scale,  the  secondary 
triads  will  appear  as  follows : 


iF=li= 


iio     N.  B.  IV 


PI 


V       VI     VI  lO 


'Y\\Q  second  degree  gives  a  dhniiiisJicd  triad,  similar  to  that  already 
found  on  the  seventh  degree  of  the  major  scale ;  a  diminished  triad  is 


MANUAL  OF  HARMONY. 


45 


also  found  upon  the  seventh  degree.  The  sixth  degree  forms  here  a 
major  triad.  The  third  degree  produces  a  new  form  of  the  triad. 
It  has  a  fnajor  third  and  an  augmented  fifth  and  is  known  as  the 
augmented  triad. 

The  peculiar  nature  of  this  chord  renders  its  connection  with  other 
chords  in  the  same  key  very  difficult ;  therefore,  it  can  seldom  be  used 
as  \hQ  fundamental  harmony  of  the  third  degree  of  the  minor  scale. 
The  following  examples  show  this  : 


/. 


55. 


1 


EEiEbiESEl^pfe=l3iEfil^^l 


;i^^ii^ii^ii^:] 


IlO 


Of  these  examples,  those  under  cand  e  will  be  the  most  useful.     The 
introduction  of  this  chord  is  still  more  difficult : 


56. 


^3*^li=S?^l?^#i3daJi^d 


&-  -G>-  -a- 


:s=^ 


iio 


VI 


Its  introduction  is  the  most  agreeable  when  the  augmented  fifth  has 
been  heard  in  the  previous  chord,  that  is,  has  been  prepared,  as 
under  d. 

Remark. — There  seems  to  be  something  peculiarly  foreign  in  the  triad  on  the  third 
degree,  whether  in  the  major  or  minor  scale,  so  that,  even  when  it  appears  simply  as 
a  minor  triad  in  the  major  scale,  it  is  very  difficult  to  connect  it  naturally  with  other 
chords,  and  is  therefore  seldom  used. 

Most  of  the  practicable  chord-connections  shown  above  will  occur 
in  other  situations  which  will  not  allow  the  augmented  triad  to  be 
recognized  as  the  triad  belonging  on  the  third  degree  of  the  minor 
scale.  The  augmented  triad  whicli  is  so  much  used  in  modern  music, 
belongs  to  the  chromatically  altered  chords,  and  will  be  explained  in 
Chap.  X,  on  Altered  Chords. 


46 


MANUAL    OF  HARMONY, 


Application. 

The  principles  concerning  the  connection  of  harmonies  and  the 
leading  of  voices  which  have  been  so  far  developed,  will  be  particu- 
larly applicable  to  the  connection  of  the  primary  chords  in  minor. 
What  was  said  regarding  the  progression  of  the  leading  tone,  comes 
very  prominently  into  view  in  consequence  of  the  step  of  an  aug- 
mented second  occurring  between  the  sixth  and  seventh  degrees  of 
the  minor  scale,  which  step  has  to  be  avoided  either  ascending  or  de- 
scending as  un?nelodious,  if  both  tones,  which  include  the  interval 
of  an  augmented  second,  belong  to  different  harmonies^  e.  g. 


57. 


i± 


I 


VI 


Therefore,  in  connecting  the  triads  of  the  fifth  and  sixth  degrees, 
which  is  a  very  common  progression,  it  will  be  necessary  to  carry  the 
leading  tone  upward,  in  consequence  of  which  the  triad  on  the  sixth 
degree  will  appear  with  its  third  doubled^  e.  g. 


i 


& 


H: 


:te 


i^gi^a 


9i=^ 


m 


VI 


VI 


VI 


VI       V 


VI 


Thus,  it  would  be  impossible  to  present  correctly  the  example  given 
under  57,  ^,  without  making  use  of  an  intermediate  tone,  as  for  ex- 
ample : 


i 


-fe- 


1 


i 


MANUAL  OF  HARMONY. 


47 


Remark. —  Practice  deviates  from  this  rule  in  certain  special  cases.  But  it  will  he 
■well  to  become  accustomed  to  the  above  leading  of  the  voices,  because  we  must  not 
overlook  the  fact  that  every  deviation  from  the  rules  in  practice  should  be  only  a 
well  founded  exception,  whereas  the  observance  of  them  can  be  cited  in  numberless 


Exercises  in  Connecting  the  Triads  of  the  Minor  Scale. 


aE$: 


ilii 


:H 


I      I  <y — (^ 


si^EpJEj^jj^liajp^^a 


6.         6J 


^^^^T^TT^^t-P-^ml^^^H 


%^i-=^^^^m^^$m 


t^ 


m^=^m^;m^-v^m^M:i^E^^^^ 


10. 


6  ,      f, 


11-  3        B    5B 


mi^^^P^^^0s^mm^^^Wf^^^¥?m 


12. 


t         B^ 


ai^3=J=FTPFT1f=^ 


i 


=P=i==^ 


Remarks  on  these  Exercises. 

A  chromatic  sign  over  a  bass  note  without  any  figure,  as  in  the 
third  measure  of  the  first  exercise,  has  reference  always  to  the  third 


48 


MANUAL    OF  HARMONY 


of  the  bass  note.  This  raising  of  the  third  in  the  dominant  chord,  is 
the  raising  of  the  leading  tone  previously  spoken  of,  and  is  of  fre- 
quent occurrence  in  the  minor  mode. 

As  a  rule,  the  triad  is  ViO\.  figured  in  thorough-bass  notation,  when 
the  bass  has  the  fundamental,  unless  there  are  special  reasons  for  mark- 
ing it  with  3,  5,  8,  |,  or  in  full,  by  | .  In  the  third  and  sixth  exercises 
the  augmented  triad  has  been  introduced  and  the  "  sj  "  placed  over 
the  bass  note  signifies  that  the  fifth  must  be  sharpened,  as  it  is  the  leading 
tone,  as  well  as  the  augmented  fifth  of  the  triad.  The  figures  3,  5,  or 
8  over  the  first  bass  note  of  some  exercises  indicates,  as  has  been  said 
before,  its  position.  If  there  be  no  figure  over  it,  the  soprano  must 
take  the  octave  of  the  bass. 

The  fundamental  principles  thus  far  developed  will  be  illustrated 
by  the  working  out  of  an  exercise.  For  this  purpose  we  select  the  first 
exercise  of  No.  60. 


61. 


Here  the  first  principle  of  the  connection  of  chords  (by  connecting- 
tones  in  the  same  voice)  is  observed  throughout,  and  consequently  the 
alto,  at  N.  B.,  makes  the  forbidden  step  of  an  augmented  second  from 
F  to  G#. 

In  order  to  avoid  this  defect,  the  alto  must  be  led  from  F  to  E,  the 
soprano  from  B  to  G|!|,  and  the  tenor  by  a  skip  from  D  to  B,  thus : 


i^i=#Mi 


•s^-       -<^- 


=1 


11° 


or  the  soprano  retains  the    B  while  the  tenor  falls  from  D  to  G^,  and 


MANUAL  OF  HARMONY. 


49 


the  alto  from  F  to  E,tluis  quitting  the  close  position,  while  the  follow- 
ing harmony  is  brought  into  open  position. 


-^^ 


IB 


^t 


^r 


Note. — The  best  way  to  overcome  the  difficulties  in  connecting  the  triad  of  the 
second  degree  with  that  of  the  fifth  (ii — V  or  11° — V),  in  major  as  well  as  minor, 
is  to  remember  to  lead  all  the  upper  voices  dmvnzuard  from  the  second  degree  triad  to 
the  next  chord.  By  taking  particular  notice  of  ihe" indications"  vih.&n  writing  them 
under  the  basses  (  and  they  should  a/wwrj  be  placed  there  be/ore  beginning  to  work  out 
the  exercise),  the  1 1 — V,  or  1 1°— V,  which  occurs  constantly,  will  serve  to  remind  the 
student  of  the  correct  manner  of  leading  the  voices. — Ed. 

Before  proceeding  to  the  further  employment  of  the  triads,  we  here 
give  a  view  of  all  the  chords  thus  far  found. 


View  of  All  Triads  of  the  Major  and  Minor  Scales. 

Major. 


fe 


III      IV 


I 


Minor. 


no    III'     IV 


VI    viio 


Major  triads  are  found 

In  major. 


E^: 


-a — 
IV 


m 


t^ 


±sz 


VI 


Minor  triads 


In  major. 


m 


5©  MANUAL    OF  HARMONY. 

Diminished  triads 

In  major.  In  minor. 


^^^l^jEEfel 


VI 1° 


IlO  vilO 


Augmented  triad 


^ 


III' 


CHAPTER  III. 


THE    INVERSIONS    OF    THE    TRIADS. 


The  Chord  of  the  Sixth,  the  Chord  of  the  Sixth  and  Fourth. 

The  employment  of  the  triads,  as  well  as  all  fundamental  chords, 
is  not  confined  to  the  positions  shown  in  the  foregoing  examples,  where 
\h&  fundamental  alone  is  used  as  the  bass.  The  third  ox  Jifth  of  the 
original  chord  may  also  serve  as  the  bass.  Thus  arise  transforma- 
tions of  the  fundamental  chords,  which  are  termed  inversions  of  the 
chord. 

Remark. — It  should  be  particularly  noticed,  that  here  only  a  change  of  the  bass  ta 
another  interval  of  the  chord  is  spoken  of,  and  the  transpositions  of  the  other  voices 
into  close  and  open  position,  and  to  various  intervals,  previously  mentioned,  do  not 
alter  the  chord  essentially. 


Two  inversions  of  the  triad  are  possible : 
a.     When  the  bass  takes  the  third  of  the  triad, 
formed  is  called  the  chord  of  the  sixth. 


the  chord    thus 


65. 


m 


Fundamental  chord.    Chord  of  the  sixth. 


Third 
of  the  fundamental  chord. 


b.     When  the  bass  takes  the  Jifth  of  the  triad,  there  is  formed  the 
chord  of  the  sixth  and  fourth. 


MANUAL  OF  HARMONY. 


51 


I 


Fundamental  Chord 

chord.  of  the  sixth  and  fourth. 


Fifth 
of  the  fundamental  chord. 


The  chord  of  the  sixth  is  indicated  by  6  over  the  bass  note,  that  of 
the  sixth  and  fourth  by  | ;   e.  g. 


67. 


m 


C 
C:    I 


It  should  be  observed  that  the  Roman  numerals  under  the  bass 
continue  to  indicate  the  degree  of  the  scale  on  which  the  fundamen- 
tal is  situated.,  and  do  not  refer  to  the  position  of  the  bass. 

Thus,  in  Ex.  67,  the  three  chords  are  all  indicated  by  I,  although 
the  bass  of  each  is  on  a  different  degree  of  the  scale,  because  they  are 
all  derived  irom  one  and  the  same  fundamental,  namely,  C. 

Similar  inversions  may  be  derived  from  all  the  triads. 

Application. 

By  means  of  the  inversions  of  chords,  the  harmony  obtains  greater 
variety,  and  the  progression  of  the  individual  parts,  and  especially  of 
the  bass,  becomes  more  flow^ing. 

According  to  the  rules  for  the  doubling  of  an  interval  of  the  triad 
(page  25),  it  will  be  better  in  the  chord  of  the  sixth  to  double  the  fun- 
damental of  the  original  chord.  The  doubling  of  the  bass  tone  must 
only  take  place  when  the  natural  progression  of  parts  seems  to 
require  it,  or  to  avoid  certain  faults.  The  leading  tone  should  never 
be  doubled,  whether  it  appears  as  third  in  the  dominant  chord,  or  as 
bass  in  the  chord  of  the  sixth. 

The  position  of  the  three  upper  voices  in  either  of  the  inversions 
depends  upon  the  natural  progression  of  the  voices,  and  has  no  influ- 
ence on  the  chord  itself. 

The  chord  of  the  sixth  can  appear  in  the  following  forms  : 


^^^m 


p^zg=|^=|^=P^g=pi^|^=P^ 


52 


MANUAL    OF  HARMONY. 


The  chord  of  the  sixth  and  fourth  occurs  less  frequently  than  the 
chord  of  the  sixth,  and  depends  on  certain  conditions  which  will  be 
explained  hereafter.  It  is  most  frequently  met  with  in  the  formation 
of  the  close   (cadences) . 

The  bass  tone  (the  original  fifth  of  the  chord)  is  most  suitable  for 
doubling,  and  the  chord  will  be  found  in  the  following  and  similar 
forms : 


69. 


W- 


§t 


"^^^^m 


i 


;l^l^^ 


;b 


No  new  mechanical  rules  are  required  for  the  connection  of  these 
chords  with  the  others ;  we  therefore  now  proceed  to  show  the  appli- 
cation of  the  inversions,  or  derived  chords,  in  the  following  exercises: 


70. 


i±SES 


Exercises. 

6  6 


6 
4  3 


^m 


'^^ 


:5=F2=P=F5: 


1=C 


£^ 


g 


wm 


6 
4  3 


6 
4  3 


m 


a±$s^ 


V=i^ 


^^ 


3       6 


E£ 


MANUAL   OF  HARMONY. 

7.  o  R  fi 


^t=E 


Hil 


^ 


S3 


i§ii=tsfe£^ia 


SS 


:I;S 


3       6       6 


■s^— ^ 


«       6       6       $ 


6       $ 


i±^=s 


6 

4  $ 


I 


^ (2- 


1=t= 


|i» 


^:E 


-^     <y- 


:^E 


<= — »■ 


i=F 


Ei!^ 


I 


Remarks  on  the  Above  Exercises. 

In  the  first  measure  of  Ex.  2,  the  position  of  the  chord  is  indicated 
by  the  figure  5  being  placed  over  the  Jirst  bass  note,  as  before  ex- 
plained. The  chord  is  therefore  to  be  written  with  the  fifth  in  the 
soprano,  or  upper  part.  If  no  figure  stands  over  the  first  bass  note  it 
is  understood  that  the  soprano  must  take  the  octave  of  the  bass. 

The  diminished  triad  (on  the  seventh  degree,  vii°)  appears  in 
its  inverted  form  as  chord  of  the  sixths  in  the  second  exercise,  second 
measure.  It  is  most  used  in  this  form.  It  may  be  remembered  that 
the  fundamental  of  this  chord,  being  the  leading  tone,  is  not  to  be 
doubled.  In  most  cases  the  third  (bass  tone)  is  doubled,  but  some- 
times the  leading  of  the  voices  occasions  the  doubling  of  the  fifth. 
The  diminished  triad  of  the  second  degree  in  minor  (ii°)  allows  the 
doubling  of  the  fii7tdame7ital^  that  not  being  a  leading  tone.  The 
progression  of  the  diminished  triad  always  depends  on  the  leading  of 
the  bass,  which  in  most  cases  is  as  follows : 


m 


«g       S* 


-G> ^ 


and  the  upper  parts  may  then  proceed  thus : 


54 


MANUAL    OF  HARMONY. 


72. 


From  the  above  examples  it  is  evident  that  the  inversion  of  the 
diminished  fifth,  that  is,  the  augmented  fourth,  does  not  require  so 
strict  a  resohition  mfour  parts  as  was  given  in  Ex.  40,  for  the  same 
interval  in  two  parts.  Thus,  in  the  first  example,  and  others,  we  see 
B  of  the  soprano  and  F  of  the  alto  progress  to  C  in  the  soprano  and 
G  in  the  alto. 


As  this  chord  has  a  similar  sound  to  the  chord  of  the  dominant 
seventh,  beginners  often  feel  the  necessity  of  leading  the  original 
diminished  fifth  downward,  even  when  it  has  been  changed  by  inver- 
sion into  the  augmented  fourth.  As  the  examples  show,  this  is  only 
necessary  when  the  diminished  fifth  appears  above  the  fundamental. 
A  progression  like  the  following  would  be  faulty  on  account  of  the 
parallel  fifths. 


It  may  here  be  observed  that  parallel  fifths,  the  second  of  ivkich  is 
diminished.,  are  allowable,  but  a  perfect  should  7iot  follotv  a  dimin- 
ished ffth. 


Not  good. 


75. 


MANUAL    01''  JIAKMONY. 


55 


The  progression  of  the  voices  In  the  inversion  of  the  diminished 
triad,  takes  a  different  form  when  the  bass  does  not  proceed  to  the 
tonic  triad.      Here  follow  a  few  chord-connections : 


Not  pure. 


VIlO        III 


VI  lO      IV 


VIlO       VI 


The  diminished  triad  on  the  second  degree  in  minor  is  capable  of 
yet  other  resolutions,  as  its  fundamental  can  be  doubled. 

The  succession  of  two  or  more  chords  of  the  sixth  on  a  bass  which 
moves  by  degrees,  as  in  Ex.  70,  No.  3,  and  others,  requires  that  one 
or  more  of  the  upper  parts  shall  move  in  contrary  motion  to  the  bass ; 
and  generally  that  the  bass  shall  be  doubled  in  one  if  not  both  chords. 


77. 


^6  MANUAL    OF  HARMONY. 

The  sequence  of  chords  of  the  sixth  in  the  fifth  and  sixth  exercises 
of  No.  70  is  best  accompanied  when  the  regular  movement  of  the 
bass  is  carried  out  in  all  the  other  parts  also,  thus : 


§ 


\ 


-6> ■-" 

etc. 


i^f^^=S^i§H 


Covered  octaves,  such  as  occur  between  tenor  and  bass  in  the  second 
and  third  measures,  are  not  to  be  avoided  in  such  cases.  In  fact,  excep- 
tional progressions  like  the  above  must  sometimes  be  permitted,  when 
to  have  adhered  strictly  to  rule  would  be  to  mar  the  proportion  of  the 
phrase. 

Remark. — That  the  principle  just  laid  down  can  be  easily  misunderstood  by  the  be- 
ginner is  evident.  But  the  statement  of  the  principle  was  unavoidable.  To  avoid  all 
possible  error,  it  may  be  added,  that  a  final  decision  on  these  points  is  only  possible 
to  a  judgment  fully  ripened  by  experience  and  practice. 

The  Signs  used  in  Thorough-Bass  Notation. 

The  figures  and  signs  in  thorough-bass  are  called  in  general,  signa- 
tures. Some  of  them  have  been  already  explained,  as  the  chro- 
matic sign  so  much  used  in  minor.  The  figuring  of  the  chords  of  the 
sixth  and  of  the  sixth  and  fourth  was  given  on  page  51.  A  stroke 
through  the  figure  is  used  when  a  chromatic  elevation  of  the  interval 
is  required,  for  example,  in  exercises  8,  9,  10,  of  Np.  70,  a  stroke 
through  the  6  :  $  ;  instead  of  which,  however,  aj^  or  H  is  often  placed 
by  the  side  of  the  figure,  for  example,  6||;or6t[,  h\.  Other  figures 
will  be  explained  later  in  connection  with  the  chords  where  they  are 
used. 

Formation  of  the  Close  through  the  Chord  of  the  Sixth  and  Fourth. 

In  the  exercises  of  No.  70  we  find  the  close,  already  mentioned, 
rendered  clearer  and  more  decided  by  the  chord  of  the  sixth  and 
fourth ;  and  it  may  be  accepted  as  a  rule  that  the  second  inversion  of 
the  tonic  triad  (chord  of  |),  w//<?/z  follozvcd  by  the  dominattt,  has  a 
strong  tendency  towards  an  authentic  close,  or  cadence. 


MANUAL    OF  HARMONY. 


57 


^^ 


C:  I 


The  chord  of  the  sixth  and  fourth  is  often  preceded  by  the  triad  on 
the  fourth  (subdominant)  or  second  degree. 


80.< 


C:  IV 


Notsvith standing  the  effectiveness  of  the  chord  of  the  sixth  and  fourth 
in  the  above  position,  and  also  in  modulations  into  foreign  keys,  yet, 
under  other  circumstances,  its  entrance  is  extremely  w^eak,  and  its  em- 
ployment is  therefore  subject  to  certain  conditions  which  will  be  men- 
tioned later. 


CHAPTER    IV. 


HARMONIES    OF    THE    SEVENTH  ;     CHORDS    OF    FOUR    TONES. 

The  chords  of  the  seventh  are  founded  upon  the  triads.  They  result 
from  the  addition  of  another  third  above  the  fifth  of  the  triad,  thus 
forming  a  seventh  from  the  fundamental : 


* 


IH 


In  addition  to  the  various  kinds  of   triads,  the   different  kinds  of 
sevenths  will  aftbrd  a  variety  of  harmonies  of  the  seventh. 


rg  MANUAL  OF  HARMONY. 

Note.— Chords  of  the  seventh  may  also  be  formed  by  adding  a  third  below  the  fun- 
damental  of  a  triad.  Thus,  the  subdominant  triad  may  be  changed  to  a  chord  of  the 
seventh  on  the  second  degree  in  the  following  manner: 


i 


^^SE 


Ed. 


C:  IV 


1I7 


General  Properties  of  the  Seventh  Chords. 

The  chords  of  the  seventh  are  not  so  independent  as  most  of  the 
triads,  but  have  a  distinct  tendency  towards  a  resolution.  On  this 
account  they  can  appear  only  in  connection  with  other  harmonies.  On 
the  other  hand,  they  render  the  relationship  of  one  chord  to  another 
more  close  and  intimate,  and  by  means  of  this  quality  offer  particu- 
larly excellent  advantages  for  the  connection  of  chords  and  leading  of 
the  voices. 

The  Chord  of  the  Dominant  Seventh  in  Major  and  Minor. 

Of  all  the  chords  of  the  seventh,  the  most  important  is  the  chord  of 
the  dominant  seventh.  It  is  also  called  the  primary  chord  of  the 
seventh.  Like  the  dominant  triad,  it  rests  upon  the  fifth  degree,  and 
is  formed  precisely  alike  in  major  and  minor,  namely,  from  the  major 
triad  and  minor  seventh  : 


i 


gEii^si 


II 


C:  V 


V7 


V7 


Its  fundamental  position  is  indicated  by  a  7  over  the  bass  note,  and 
in  our  system  of  notation  by  V7  : 


^t 


I 


C:  V7 


G:  V7 


The  relation  which  the  dominant  triad  bears  to  that  of  the  tonic  has 
been  already  shown  by  means  of  the  close  (see  page  33),  and  the 
impression  of  finality  created  by  the  cadence  will  be  much  strength- 
ened by  the  addition  of  the  seventh.  The  following  connection  of 
chords  will  exhibit  the  formation  of  the  close : 


MANUAL  OF  HARMONY. 


59 


C:  V7 


a:  V7 


Remark. — Observe  that  the  chord  of  the  tonic  which  follows  the  dominant 
seventh  cliord  is  incomplete;  in  both  cases  the  fifth  is  omitted.  The  reason  of  this 
will  be  perceived  from  what  follows. 

The  marked  tendency  towards  a  resting-place  or  close,  inherent  in 
these  cliords,  and  their  consequent  connection  with  a  triad,  is  called 
resolution  of  the  chord  of  the  seventh  (cadence). 

If  the  chord  is  resolved  into  the  tonic  triad,  as  in  Ex.  84,  or  in  a 
similar  manner,  it  is  called  a  closing  cadence. 

The  progression  of  the  intervals  of  the  chord  of  the  seventh  will 
make  necessary  some  important  remarks. 

First,  we  regard  the  closing  cadence  as  the  regular  resolution  of  the 
dominant  seventh  chord  especially. 

The  seventh,  as  the  essential  interval  of  the  chord,  is,  from  its  re- 
lation to  the  fundamental,  restricted  to  a  stated  progression.  The 
progression  of  the  bass  being  given,  an  upward  resolution  of  the  sev- 
enth would  seem  impossible  : 


85. 


i 


even  if  a  third  voice  be  added,  as  at  b ;  whereas  its  do-wnvjard  move- 
ment will  be  entirely  satisfactory  to  the  ear. 

Since  the  progression  of  the  fundamental  by  a  skip  upward  of  a 
fourth  or  downward  by  a  fifth  is  already  determined,  the  leading  of 
the  third  ?^x\djifth  of  the  chord  of  the  seventh  remains  to  be  considered. 

T/ie  third  of  the  chord  of  the  dominant  seventh  is  ahvays  the 
leading  to?ze  of  the  scale;  its  natural  tendency  is,  therefore,  upward 
a  half  step  to  the  tonic.  Thus,  in  the  following  example,  a  is  more 
satisfactorv  than  b : 


6o 


MANUAL    OF  HARMONY. 


87. 


iszil: 


=]=:^=l=i=:^^:g=H 


9^ 


:i^i^H 


In  Ex.  87,  <5,  the  third  is  given  to  the  upper  voice,  which  makes  the 
unnatural  progression  very  conspicuous.  If  the  third  appears  in  a 
middle  voice,  this  leading  becomes  less  unpleasant,  e.  g. 


^^m 


im 


V7    I 


This  downv^^ard  leading  of  the  third    (leading  tone)    is    therefore 
allowable  under  the  following  conditions : 

a.     When  it    lies  in  a  middle  voice.,  but  not  when  in  an  upper 
part,  e.  g. 

Seldom  used. 


^= 


-i 


h.     When  the  bass  moves  in  contrary  motion  with  it,  e.  g, 
a.  b.         Not. 


90. 


i 


a^ 


The  reason  for  the  second  rule  is  evident,  if  we  observe  the  covered 
fifths  between  alto  and  bass  in  the  last  example  at  b. 


MANUAL    OF  JIARMONY. 


6i 


The  leading  of  thcffth  of  tlie  chord  of  the  seventh  is  free.  While 
it  usually  descends  one  degree,  through  the  downward  pressure  of  the 
seventh,  the  progression  of  the  voices  may  require  it  to  ascend,  as  in 
Ex.  88,  3,  where  the  D  of  the  soprano  is  led  to  the  E  in  the  next  chord. 

If  we  summarize  these  remarks,  the  following  rules  are  established 
for  the  regular  resolution  of  the  chord  of  the  seventh,  and  for  the 
closing  cadence  especially  : 

The  seventh  descends  a  diatonic  degree  ; 

The  fundamental  skips  a  fourth  upward  or  a  fifth  downward ; 

The  third  ascends  a  degree  in  contrary  motion  with  the  seventh ; 

The  fifth  can  either  ascend  or  descend  one  degree. 

Remark.— The  relationship  of  the  third  and  seventh  to  one  another  recalls  what 
has  already  been  said  on  the  resolution  of  the  diminished  fifth,  this  interval  being  again 
found  and  similarly  treated  in  the  chord  of  the  dominant  seventh  : 


Application. 

The  chord  of  the  dominant  seventh,  as  thus  far  known  to  us,  seldom 
occurs  in  the  middle  of  a  composition,  but  when  it  is  so  employed  the 
feeling  of  a  perfect  close  should  be  avoided. 

This  result  may  be  attained  by  giving  the  seventh  to  the  upper 
part,  which  will  render  the  close  incomplete ;  or  by  causing  the  dom- 
inant seventh  chord  to  fall  upon  the  accented  part  of  the  measure, 
whereas,  in  the  perfect  close  (complete  cadence)  the  tonic  triad  must 
fall  l:here.      (See  Ex.  25.) 

The  chord  of  the  seventh  often  appears  incomplete  by  the  omission 
of  one  interval,  generally  the  fifth.  The  third  is  very  seldom  omitted, 
and  the  omission  of  either  the  fundamental  or  seventh  would  of  course 
destroy  its  identity. 


Seldom. 


91. 


i 


-,S^2_ 


W^ 


62 


MANUAL    OF  HARMONY. 


In  the  above  example,  at  a,  ^,  and  c/,  the  fifth  is  omitted ;  at  c,  the 
third ;  and  in  each  case  the  fundamental  is  doubled  instead,  by  which 
means  the  closest,  connection  is  obtained  with  the  following  chord 
through  the  tone  which  remains  stationary,  and  allows  the  tonic  triad 
to  again  appear  complete.  This  could  not  be  the  case  if  the  funda- 
mental of  the  seventh  chord  were  not  doubled.     (See  No.  84.) 

The  following  remark  concerning  the  omission  of  an  interval  in  the 
chord  is  added  : 

Through  the  leading  of  the  voices,  a  chord  may  appear  inco?>ipIete ; 
in  most  cases  the  omitted  interval  will  be  t\\ejift/i  of  the  fundamental 
chord. 

Exercises. 


.Eiii: 


^B 


-6* -(2- 


=f=t 


3.      3 


S^E 


F — \~V^^=^^ 


^m 


^=^=x 


6 
4  7 


?=3= 


I 


5. 


:g±$: 


2=E 


6         7 

4         t 


I 


-^ 5- 


p-=^-±t=^^ 


:iSE 


^^m 


t^ 


6' 

6  ,        4< 

t=l: 


t=n 


%-■• 


^g!,1i8E^g=^r=^=ff^:.g|EEJEpEi 


6  6 
6      4  37 


MANUAL    OF  HARMONY. 


-«>-      P. 


SSsiS^^^^I 


6  7 


Ha 


10. 


7 

6       Q 


§^g-rf--=^^=igi£5=^^gi^^-^£BI 


l#jte 


6  7 
6      X 


m 


Note.  In  the  sixth  measure  of  Ex.  4,  of  the  above  exercises,  the  same  division  of 
the  measure  into  two  halves  takes  place  which  has  been  noticed  before  in  No.  70. 
Here  the  first  half  of  the  measure  requires  the  tonic  (§)  followed  by  the  chord  of  the 
seventh  in  the  last  half  of  the  measure.  In  the  fifth  measure  of  Ex.  7,  the  second 
chord  \s  that  of  the  tonic  (|),  then  follows  the  dominant  triad,  \\.?>  fifth  passing  after- 
wards (by  skip)  to  the  seventh.  It  should  be  remembered  that  accidentals  placed  over 
bass  notes  always  refer  to  the  third  oi  that  note  ;  when  placed  by  the  side  of  figures, 
they  mdicate  that  that  interval  above  the  ^^.fjmust  be  raised  or  lowered,  as  the  case 
may  be. — Ed. 


CHAPTER   V. 


THE    INVERSIONS    OF    THE    CHORD    OF    THE    SEVENTH. 

The  inversions  of  the  chord  of  the  seventh  are  formed  in  the  same 
manner  as  those  of  the  triad. 

The  first  inversion  is  formed  by  taking  the  third  of  the  chord  for 
the  bass;  the  second,  by  giving  the  fifth  to  the  bass;  and  the  thirds 
when  the  bass  receives  the  original  seventh. 


54 


MANUAL    OF  HARMONY. 


In  close  position  the  inversions  appear  thus : 


83. 


S£ 


_^ffi_ 


'G7       G7       G7        G7 

A  comparison  of  these  inversions  of  the  chord  of  the  seventh,  with 
those  of  the  simple  triad,  will  show  their  relative  positions: 

6 
6  4 

-jg— 


t(t) 


2(22) 


^^ 


G7 


G7 


G7 


G7 


These  derived  chords  receive  their  names  from  the  intervals  which 
are  found  over  the  bass  : 

T\\^  first  inversion  is  called  the  chord  of  the  sixth  and  fifth. 

The  second:  the  chord  of  the  sixth,  fourth,  and  third,  or  briefly, 
the  chord  of  the  fourth  and  third. 

The  third:  the  chord  of  the  sixth,  fourth  and  second,  or  briefly, 
the  chord  of  the  second. 

The  thorough-bass  figuring  may  be  seen  above,  in  Ex.  94. 

As  is  the  case  with  the  inversions  of  the  triad,  these  chords  de- 
pend only  on  the  position  of  the  bass,  and  the  upper  voices  may  be 
arranged  in  various  ways,  e.  g. 


MANUAL    OF  HARMONY. 


Application. 


65 


The  regular  progression  (resolution)  of  these  derived  chords  is 
founded  on  that  of  the  original  chord. 

As  the  dissonance,  the  seventh,  caused  the  progression  of  it  in  one 
direction,  the  tendency  to  the  same  progression  will  exist  in  the  de- 
rived chords  where  the  fundamental  and  seventh  appear  again,  or  the 
two  tones  become  seconds  bv  inversion. 


Progression  of  the  Chord  of  the  Sixth  and  Fifth. 

In  the  chord  of  the  sixth  and  fifth,  the  original  seventh  still  forms 
a  dissonance  with  the  bass,  but  in  this  case  it  is  a  diminished  fifth,  the 
resolution  of  which  has  already  been  explained . 


■m 


;l:l 


The  resolution  of  the  complete  chord  of  the  sixth  and  fifth  will  nat- 
urally be  as  follows : 


m 


^^^^^-_ 


^1 


G7 


That  is,  all  the  voices  (except  the  fundamental  G)  will  have  the  same 
progression  as  they  had  in  the  original  chord.  The  fundamental 
remains  stationary,  as  it  is  not  suited  to  the  character  of  an  upper  or 
middle  part  to  proceed  by  such  large  intervals  as  the  fundamental  did 
when  it  appeared  as  bass  of  the  original  chord.  That  the  G,  however, 
forms  the  foundation  of  this  connection  of  harmony,  is  shown  by  the 
marking  G7 — C,  in  Ex,  98. 

Remark.— Different  progressions  of  the  fundamental,  due  to  a  freer  leading  of  the 
voices,  are  not  hereby  excluded,  but  there  must  be  an  inner  connection  between  the 
chords. 


^  MANUAL    OF  HARMONY. 

Progression  of  the  Chord  of  the  Sixth,  Fourth,  and  Third. 

This  chord  contains  between  its  component  parts  not  only  the  inter- 
val of  a  seventh,  or  its  inversion,  the  second,  but  also  that  of  the 
diminished  fifth,  or  its  inversion,  the  augmented  fourth. 


-^ 


[-1 


1 


The  resolution  of  this  chord  follov^^s  thus 


^i=^'- 


^^ 


G7        C  G7  C 

The  bass,  being  the  original  fifth,  is  free  to  move  both  ways. 


Progression  of  the  Chord  of  the  Second. 

This  chord  has  the  peculiarity,  that  the  dissonances  of  the  original 
chord,  the  seventh  and  the  diminished Jifth,  can  only  appear  in  their 
inverted  form,  as  second  beloiv^  and  augmented  fourth  below. 

The  resolution  of  this  chord  is  to  a  chord  of  the  sixth  on  the  tonic : 


lOl 


It  will  be  seen  that  all  these  resolutions  are  based  upon  the  natural 
progression  of  the  dominant  seventh  chord  (cadence),  since  we  find 
throughout  the  same   marking  of  the  fundamentals,  G7  C,  or  V7  I. 

Therefore,  these  resolutions  will  of  themselves  form  cadences,  but 
not  so  complete  as  those  mentioned  before.  As  those  were  called 
perfect  cadences,  we  describe  these  as  imperfect  candences. 


MANUAL   OF  HARMONY. 


67 


Note. — In  the  inversions  of  the  chord  of  the  seventh  all  of  the  four  intervals  are 
usually  present,  the  three  upper  voices  taking  those  not  required  by  the  bass,  which 
latter  is  seldom  doubled  in  four-part  harmony. — Ed. 

View  of  the  Natural  Progression  of  all  Inversions  of  the  Chord  of 
the  Dominant  Seventh  in  Various  Positions. 

a.     THE   CHORD    OF   THE    SIXTH   AND    FIFTH. 


102.<  \ 


^^^1: 


P^E^E 


j^^H->g  j=^-5^  j^^- 


Gt        c 


:H 


THE   CHORD   OF   THE   SIXTH,   FOURTH   AND   THIRD. 
Or. 


g.-^*i=tesi^l=J^fcl 

4                               4                       4 
3                                 3           6            3 

->^     "'^ a. 5i 2^: a — 1 

Gv 


% 


<=»=-«- 


«— =.2: 


li^^l^^ 


i 


c.    THE   CHORD    OF   THE   SECOND. 


g^^^^^^i^ 


G>^^^ 


^^li^ 


,6  2  6 


^^7^1 


G7       C 


68 


MANUAL  OF  HARMONY. 

Exercises  for  using  these  Chords. 

6 

6  6  ( 


32  6 


6 

4  7 


6 

47 


3±^ 


I 


^m 


6 
5.        3  5 

^ -#^ 


i=^:       ' 


87 

6  % 


t=T 


g        eJ- 


-0 ^ 


=F==t= 


2         6$ 


6  7 

4« 


asiE 


-Ig— t— fg — s)- 


4 

3        6 


§i^ 


=^=F!=2- 


£Ef^lg^^%^ 


6  7 

6  4  J 


^ss$^^ 


^  4 

6  t  „  3  2  6  3 


6  7 

6  4$ 


i 


WP 


6 
5  6         2  6  ,457 


-S* -t-!g  &j  <g- 


10.„         3         2         6        ♦ 


Il2- 


f*f 


MANUAL  OF  HARMONY. 


69 


Note. — In  the  seventh  measure  of  the  last  exercise  will  be  found  the  augmented  triad 
on  the  3d  degree  of  A  minor,  introduced  by  leading  the  soprano  from  a\i,  through 
^  to  /  The  g\L  could  also  be  regarded  as  a  "  passing  note."  Worked  out,  the  pas- 
sage will  appear  thus : 


=EiE^ 


*      \wf 


I 


Ed. 


Ill' 


CHAPTER   VI. 

SECONDARY    HARMONIES    OF    THE    SEVENTH. 

Whereas  with  the  triads,  three  primary  chords  are  necessary  to  form 
the  key,  the  tonic  being  the  central  point,  only  one  primary  chord  of 
the  seventh.,  that  of  the  domifiant  seventh  is  needed,  the  contents  of 
which  alone  makes  the  key  certain,  and  whose  resolution  to  the  tonic 
triad  represents  it. 


Remark.— As  the  seventh  of  the  dominant  chord  is  also  the  fundamental  of  the 
subdominant  triad,  the  relationship  existing  between  the  two  tones  G  and  F  (  as  the 
fundamentals  of  the  dominant  triads)  to  their  common  center,  C  (as  tonic  triad), 
becomes  clear. 


70 


MANUAL    OF  HARMONY. 


Besides  this  chord  of  the  dominant  seventh,  other  chords  of  the 
seventh  are  possible  on  every  degree  of  the  major  and  minor  scales. 
Their  relationship  to  the  key  in  which  they  occur  is  certainly  undeni- 
able, but  not  so  decided  as  that  of  the  primary  chord  of  the  seventh. 

These  chords  of  the  seventh  are  called  secondary  chords  of  the 
seventh.  They  are  formed  by  simply  adding  a  seventh  of  the  funda- 
mental to  the  triads. 

a.    In  major. 


i 


3 


b.    In 


i 


N.B. 


^B 


We  find  here  chord  formations  which  have  a  somewhat  harsh  and 
foreign  effect,  because,  as  has  been  already  observed,  their  relation- 
ship to  a  fundamental  key  is  not  so  distinct  and  clear  as  that  of  the 
chord  of  the  dominant  seventh.  They  are  therefore  less  frequently 
used,  but  are  nevertheless  well  adapted  to  give  variety  and  especial  col- 
oring to  harmonic  progressions. 

Among  these  secondary  chords  of  the  seventh,  the  following  kinds 
may  be  distinguished  : 

a.     Major  triads  with  major  seventh. 

In  major.  In  minor. 


■^^ 


N.  B.     Major  triads  with  minor  sevenths  always  form  chords  of    the  dominant 
seventh. 

b.     Minor  triad  with  major  seventh. 

In  minor. 


Pfi 


Not  used  as  fundamental  harmony. 


MANUAL  OF  HARMONY. 

Minor  triads  with  minor  seventh. 
In  major. 


71 


C:  117      1117       VI7  a:  IV7 


Diminished  triads  with  a  minor  seventh. 
In  major.  In  minor. 


i 


C:  VI1O7  a:  ll°7 

Diminished  triad  with  a  diminished  seventh. 

In  minor. 


^=1^ 


a:  VII"7 
y.     The  augmented  triad  with  a  major  seventh. 


ii^ 


a:  IIIV. 

As  it  is  found  upon  the  third  degree  in  minor,  while  not  altogether 
useless  for  reasons  already  shown  in  the  case  of  the  augmented  triad, 
is  but  seldom  used,  and  ambiguous. 

Remark.— This  chord  will  be  found  again  in  Chap.  X,  with  a  different  foundation. 

Application  of  the  Secondary  Chords  of  the  Seventh  in  Major. 

Whether  the  interval  of  the  seventh  (or  its  inversion,  the  second) 
be  major,  minor,  diminished  or  augmented  (the  last  concerns  the 
second  only),  it  will  always  form  a  dissonance  with  the  fundamental, 
and  as  such  will  press  to  a  resolution. 

This  natural  resolution  will  be  the  same  as  that  given  to  the  dom- 
inant seventh  chord,  that  is,  the  seventh  will  descend  one  degree,  if 
the  fundamental  proceeds  a  fourth  upward  or  a  fifth  downward. 

Accordingly,  if  the  progression  of  the  principal  intervals  of  the 
chord  is  found. 


72 


MANUAL  OF  HARMONY. 


no  new  rules  are  needed  for  the  other  intervals ;  the  third  ascends  one 
degree,  while  the  fifth  is  free  to  move  in  either  direction. 


i 


^ 


i^ 


9t 


<^'^7. 


IV 


The  exceptional  progression  of  the  thirds  shown  at  b  in  the  above 
example,  is  in  order  to  avoid  the  covered  octaves  which  would  other- 
wise occur  in  the  regular  ascension  of  the  third  by  a  whole  step. 


;=^=l^ 


-^^^a. 


ySEE^^^ 


Whether,  however,  it  will  be  preferable  to  double  the  leading  tone 
in  the  triad  which  follows  the  seventh  chord,  as  at  107,  c,  or  to  em- 
ploy the  following  covered  fifths, 


109, 


P^^^^ 


I 


will  depend  upon  circumstances,  and  can  only  be  decided  when  par- 
ticular cases  arise. 


MANUAL    OF  JIAKMONY. 


73 


Natural  (Cadencing)  Progression  of  the  Secondary  Chords  of  the 
Seventh  in  Major. 


Of  the  first  degree.    Or. 

Not. 

:^l==feEy--S5^iN 

m—%-~^^. ^ — 

9^^^-  — .^ 

C:  I7        IV 


\ 


SS^BES^ 


Not. 


,  With  omission  of  the  fifth. 


:^^P^^=i^^ 


74 


MANUAL   OF  HARMONY. 


Of  the  third  degree. 


J^^^ 


Without  fifth. 


w^^^^^^^^m 


—  I    ^   I r~?^-\ r-7^\ r^— I — — 7tl^5^l=rzs=tl 


C:iii-     VI 


Of  the  fourth  degree  (seldom  with  this  resolution.) 

-<9 


-g— ^-,©- 


I— T=g^^^      I ^^^      I 


Not  good. 


-^-  ,  •^: 


1^^ 


9fc=s 


^^^^i 


=^F^ 


not: 
C;1V7.      vii<: 


Without  fifth. 


I 


9t 


iSS 


Of  the  sixth  degree, 


ia^^il^ir^^liiii 


g!^^^gE|^5E|^^=^|=^ig^^^g^H 


not:  not: 

6':VU      II  ~ 


MANUAL  OF  HARMONY. 


75 


)f  the  seventh  degree 


Not  good. 


^^^^^^^^mm 


9t 


^^^m^^^ 


not: 
C:  vii°7     III 


Without  fifth. 


Remark.— The  progressions  of  all  the  chords  of  the  seventh  given  above  are  neith- 
er exhaustive  in  their  positions,  nor  are  they  given  as  the  only  ones  possible. 

The  only  difficulty  in  making  such  progressions  lies  in  the  frequent  occurrence  of 
covered  fifths  and  octaves.  The  remarks  which  are  found  above,  such  as  "  not,"  "  not 
good,"  which  refer  mostly  to  the  leading  of  the  bass  (as  this  in  connection  with  the 
other  necessary  voice-movements  produces  these  faults),  are  in  many  cases  to  be  un- 
derstood from  a  theoretical  standpoint  only.  In  practice,  even  in  the  so-called  pure 
composition,  such  and  similiar  cases  must  often  be  judged  according  to  the  principle 
heretofore  stated  under  Ex.  yS,  page  56. 

Theory  not  having  yet  succeeded  in  formulating  positive  rules  for  all  cases  of  the 
kind,  the  true  and  the  false,  that  which  is  admissible  or  inadmissible  in  this  respect 
can  only  be  ascertained  through  thorough  harmonic  culture  and  a  correct  musical 
ear. 


Of  the  Peculiar  Resolution  of  the  Chord  of  the  Seventh  of  the 
Seventh  Degree. 

In  the  above  table,  under  No.  no,  the  same  resolution  has  been 
given  to  all  the  chords  of  the  seventh,  including  that  on  the  seventh 
degree,  v^^hich  has  been  resolved  into  the  third  degree.  In  each  case 
the  fundamental  proceeds  a  fourth  upward  or  a  fifth  downward. 
This  progression  is  the  less  frequent  one,  and  is  mostly  used  when 
the  voices  maintain  a  regular  movement.,  as  in  sequences.  A  more  usual 
progression,  however,  of  this  chord,  is  that  founded  on  the  resolution 


y6  MANUAL  OF  HARMONY. 

of   the    diminished    triad   (from  which  this  chord    of  the  seventh  is 
derived) ,  which  is  to  the  tonic  triad. 


i 


i 


i 


^z; 


C:  viio 


VIlO         I 


vr.f,   I 


The  above  examples  show  that  the  tendency  of  the  diminished  triad 
towards  the  tonic  triad  is  not  changed  by  the  addition  of  the  seventh, 
but  is  rendered  even  more  decided. 

Observe,  also,  that  when  the  chord  appears  in  the  above  position, 
the  third  of  the  following  triad  must  be  doubled,  as  at  No.  iii,  b^  or 
parallel  perfect  fifths  would  arise,  as  at  No.  112,  a. 


12. 


'^^^^ 


^ 


^ 


or  the  third  of  the  chord  must  skip,  as  at  <5,  a  leading  of  the  tenor 
which  frequently  occurs,  and  which  is  very  effective  notwithstanding 
the  covered  octave  between  soprano  and  tenor. 

This  chord  has  the  peculiarity  that  its  only  satisfactory  position  is 
when  the  seventh  is  heard  in  the  upper  voice,  and  that  all  the  other 
positions,  if  not  impracticable,  appear  uncertain  and  indistinct  in  their 
effect. 


i 


9fc 


i 


MANUAL  OF  HARMONY. 


77 


Remark. — Whether  the  reason  of  this  lies  in  the  fact  that  the  seventh  with  the 
above  resolution  has  the  character  of  the  ninth,  which,  though  similar  to  the  seventh, 
is  much  more  comprehensive  and  does  not  admit  of  a  middle  position  in  the  chord, 
cannot  be  further  discussed  here. 

Note. — Many  theorists  give  this  chord  as  a  chord  of  the  ninth  on  the  dominant 
with  the  fundamental  omitted. — Ed. 


The  Freer  Treatment  of  the  Third  and  Fifth  in  the  Chord  of  the 
Seventh. 

Different  progressions  of  these  intervals  have  already  been  used  in 
the  previous  connections  of  chords.  Thejifth  is  led  in  either  direc- 
tion ;  also,  the  third  is  led  a  degree  upward,  or  by  a  skip  a  third 
dovv^nvirard.  This  was  generally  for  the  purpose  of  avoiding  covered 
fifths  and  octaves. 

When  these  faulty  progressions  do  not  intervene,  the  thirds  espe- 
cially, can  move  differently  still,  by  means  of  which  the  movement  of 
the  voices  becomes  more  free  and  independent,  e.  g. 


b.  Not  good. 


^ 


1  14.< 


;l= 


^  »  "^ •- 


If  the  position  admits  of  it,  this  leading  is  possible  also  in  the  middle 
voices,  as  at  c. 

The  progression  of  the  soprano  at  b  is  not  good  on  account  of  the 
skip  of  an  augmented  fourth — from_/"to  b — which  is  caused  by  it. 

The  skip  from  the  fourth  to  the  seventh  degree  is  called  the  tri- 
tone,  because  it  contains  three  whole  tones.  Regarding  this  more 
hereafter. 

Different  progressions  of  the  fifth  are  only  possible  when  the  move- 
ment of  the  bass  differs  from  that  above  given,  which  is  that  of  a  fun- 
damental. If  we  seek  for  other  chord-connections  than  those  hitherto 
used,  still  other  progressions  of  the  voices  will  show  themselves. 


Hg  MANUAL  OF  HARMONY. 

The  Preparation  of  the  Seventh. 

The  progression  of  the  chords  of  the  seventh  has  been  spoken  of, 
but  nothing  has  been  said  of  their  introduction. 

The  harsh  effect  produced  by  the  entrance  of  many  of  the  disso- 
nances, and  especially  of  the  seventh  of  the  secondary  chords  of  the 
seventh,  renders  a  careful  introduction  of  them  necessary,  which  con- 
sists in  their  being  prepared. 

A  tone  is  prepared,  when  it  has  been  heard  in  the  preceding  chord., 
as  a  consonance,  and  in  the  satne  voice.,  so  that  it  can  be  connected 
by  a  tie. 

Such  a  preparation  of  a  tone  has  already  been  had  in  the  first  chord- 
connection  shown,  e.  g. 


1  15. < 


i 


It  may  be  said  here  that  the  C  of  the  soprano  in  the  second  chord 
is  prepared  by  the  C  in  the  first  chord.  The  same  applies  to  the  G 
of  the  alto  in  the  next  example. 

The  necessity  of  the  preparation  of  the  sevenths  is  not  due  alone  to 
their  harshness  when  heard  without  preparation,  but  particularly 
from  the  character  of  harmonic  relationship  and  connection  of  two 
successive  chords,  which  is  a  prominent  characteristic  of  sevenths, 
and  which  would  not  be  felt  without  their  preparation. 

The  preparation  of  the  seventh  may  take  place  in  the  following  or 
any  similar  manner : 


116./ 

1 


^iSiiSi^rap 


FT-^i=Qa^Ef 


EEt^^l^ 


S 


C:  V         I,    IV 


ly^   IV  IV  Ily    V  I 


II      V,   I 


MANUAL    OF  HARMONY. 


79 


iiii^^^[ 


r^r 


I    I 
^  ^ 


-^ 


^^m 


C:in    I\'       viio     V      in. 


IV    viio-     I 


In  each  of  the  above  examples  the  tone  which  is  bound  to  the  next 
one  following  by  means  of  a  tie,  forms  the  preparation  of  the  seventh. 

In  constructing  such  preparations  the  following  rules  must  be  ob- 
served : 

a.  The  preparation  must  fall  on  the  unaccented  part  of  the  measure 
(Arsis). 

/;.  It  must  be  of  at  least  equal  duration  with  the  seventh  by  which 
it  is  followed.      It  may  be  longer,  but  never  shorter,  e.£^. 


-A- 


m 


=t=g: 


17. 


I 


Remark. — The  preparation  of  the  sevenths  forms  one  of  the  most  important  parts 
of  the  theory  of  harmony,  and  is  to  be  carefully  and  diligently  practiced,  because  upon 
it  depends  the  most  important  feature  of  the  inner  and  most  intimate  harmonic  con- 
nection. 

Although  here  also  exceptions  on  this  point  may  be  found  in  practice,  still,  it  must 
be  remembered  that  they  are  only  exceptions,  and  do  not  disprove  the  importance  of  the 
principle  of  harmonic  connection.  Such  exceptions  can  only  be  judged  by  their  posi- 
tion and  relation  to  the  situation  as  a  whole. 

These  exceptions  occur  mostly  with  the  minor  sevenths,  as  those  on  the  second  and 
seventh  degrees,  which  are  less  harsh,  and  may  always  be  improved  by  good  leading 
of  the  voices. 

The  chord  of  the  dominant  seventh,  however,  being  less  foreign  to 
the  key,  does  not  always  require  preparation.  The  note  forming  the 
interval  of  the  seventh  in  this  chord  may  be  freely  introduced,  but  in 
this  case  the  J'lindamenia/  of  the  chord  should  be  already  present  in 
the  previous  chord.,  in  order  to  preserve  the  progression  of  the  parts 
pure  and  free  from  harshness. 


8o 


MANUAL    OF  HARMONY. 


4^J— J- 


i^J 


w 


T — r 


EK 


Hffi ^ 


in 


^-rr 


C:  I 


Note. — In  each  of  the  above  examples  the  fundamental  of  the  chord  of  the  dominant 
seventh  is  present  in  the  previous  chords,  in  the  alto  ;  the  seventh  is  therefore  allowed 
to  appear  without  preparation. — Ed. 

The  chord  of  the  seventh  on  the  seventh  degree  of  the  major  or 
minor  scale  may  also  be  used  without  preparation. 


6 

4  7 


1  19. 


S±^ 


1 — rg- 


:^=t=: 


m 


1 


6 

4         7 


m 


m 


^ii$Efe?E3^£^ 


i 


fg — s> — <g- 


gte: 


-«?-      7 


^^ 


I 


i=:^ 


Ss 


F=F 


^ 


I 


sSfe: 


^1 


I  1--^  t 


1=^ 


gS 


r-^-nr 


^^m 


1  5 
6        6        7       8  7 


ES 


-fi^ 2^- 


i 


MANUAL    OF  HARMONY. 


8i 


fflr^ 


:4='<^?S" 


4^ 


^^ 


i 


The  Connection  of  the  Chords  of  the  Seventh  with  each  other. 

In  the  previous  examples  every  chord  of  the  seventh  has  been  re- 
solved into  the  triad  on  the  fozirth  degree  above,  or  which  is  the  same 
thing  fundamentally,  a  fifth  below.  Instead  of  the  triad,  a  chord  of 
the  seventh  can  also  follow^  the  fundamental  of  the  new  chord  being 
likewise  a  fourth  above  that  of  the  first.  No  change  takes  place  in 
the  resolution  on  this  account,  but  the  third  in  the  first  chord  of  the 
seventh  remains  stationary  in  order  to  prepare  the  seventh  in  the 
next  chord,  e.  g. 


^ 


^- 


V7 


IV 


Here  the  third  of  the  dominant  chord,  the  B,  remains  stationary  and 
prepares  the  seventh  of  the  next  chord. 

The  peculiarity  of  the  resolution  of  one  seventh  chord  into  another 
is,  that  in  one  of  the  chords  the  fifth  will  always  be  lacking.  When 
several  chords  of  the  seventh  follow  each  other,  the  omission  of  the 
fifth  will  take  place  in  each  alterjiate  chord. 


82 


MANUAL    OF  HARMONY. 


121., 


^^^ 


U-4— 4,^=^ 


s^-|-s^ 


i 


iifi^ 


7         7 

^- 


1 


1^^     I 


p'—r'^      g*- 


i 


The  following  rule  will  apply  for  progressions  of  this  kind.  When 
two  or  more  chords  of  the  seventh  follow  each  other  in  the  ftinda- 
mental  position.,  the  fifth  will  be  omitted  in  alternate  chords. 


Exercises. 

6 
6  6 


a 


.Ei* 


-^ — ■  — I f- 


2.2.. 


f=t 


6         4  2 


§Sf 


i=4: 


i 


:t=^ 


■e^—Vzi — <s^ 


ii* 


.577         77         7366  6  26         7        7, 


S^ 


-■s^-h^ 


I 


6 
6        6 


^1$-=g^^^P^g^^^^g^^^ 


7  7  7 


jatg^g^^ 


f--T=^P^^g^^^ 


=§33^ 


£ 


^ 


-&>--— ^ 


P^i 


MANUAL  OF  HARMONY. 


83 


'^^ 


^*b«i 


Application  of  the  Secondary  Chords  of  the  Seventh  in  Minor. 

The  use  of  the  secondary  chords  of  the  seventh  in  minor  is  not  so 
general  as  those  of  the  major  scale.  Many  of  them  are  either  uncer- 
tain and  ambiguous,  or  their  resolutions  produce  harsh  and  unmelo- 
dious  progressions  of  the  voices. 

With  these  last  may  be  classed  the  chord  of  the  seventh  on  the  first 
degree  of  the  minor  scale,  w'hich  if  resolved  like  those  given  above, 
would  produce  a  chord  connection  w^hich  is  not  conceivable. 


..3.| 


Remark. — Even  supposing  progressions  with  the  above  combination  of  intervals 
can  be  formed  like  this  : 


ji^te 


;i 


^fc 


n     6 

still,  it  would  hardly  prove  that  it  is  really  a  progression  of  the  chord  of  the  seventh 
on  the  first  degree  in  minor. 

The  natural  resolution  of  the  chord  of  the  seventh  on  the  secoftd 
decree  is  to  the  dominant,  and  is  much  used. 


125. 


i 


9fc 


K 


\Z^^'  |=^gE|=H^ 


1 


a:  11O7      V 


84 


MANUAL    OF  HARMONY, 


A  resolution  of  the  chord  of  the  seventh  on  the  third  degree  is  pos- 
sible ;  it  is,  however,  ambiguous,  and  belongs  rather  to  C  major  than 
to  a  mimr.      (See  Altered  Chords.) 


-f 

e>^ 

27— 



— & — 

-^- 

-n 

<^\ 

--^^^ 

"13^= 

G>— 

-&- 

=f| 

^            5? 

— 1        '^- 

==-^ 

e^  ^ 

^^ 

—  z: 

-1 

a:  IIIV.    VI  —  

It  should  be  observed  that  thejifth  in  this  chord,  as  an  augmented 
interval^  will  always  ascend  one  degree. 

The  seventh  chords  on  the  fourth  and  sixth  degrees  are  seldom  used, 
as  their  resolution  occasions  harsh  and  unmelodious  progressions. 

.^-        .£2.  Good. 


127. 


-^^ 


a:  IV7      vii*- 


T--^^ 


:|^t==^: 


"¥ 


1 


i^^^l^^^^lii^l 


The  unnatural  character  of  most  of  the  above  progressions  is  very 
apparent  and  prevents  their  general  use. 

The  seventh  degree  carries  a  very  important  chord,  generally  known 
by  the  name  of  the  chord  of  the  diminished  seventh.  A  resolution 
of  this  chord  in  the  same  manner  as  the  others  (to  a  fundamental  a 
fourth  above)  is  impossible,  as  it  would  lead  to  the  triad  on  the  third 
degree,  which  was  shown  above  to  be  doubtful  and  ambiguous. 


MANUAL  OF  HARMONY. 


85 


Instead  of  this,  its  resolution,  as  in  the  case  of  the  chord  of  the 
seventh  on  the  seventh  degree  in  major,  is  based  on  the  natural  up- 
ward tendency  of  its  fundamental,  which  is  the  leading  tone  of  the 
scale : 


li 


^^EEfs 


V1107 


c:   VI1O7 


Thus,  while  the  fundamental  of  this  chord  rises,  and  the  seventh 
falls  one  degree,  the  third  and  fifth  are  led  as  in  other  chords  of  the 
seventh,  but  the  leading  of  the  third  must  be  carefully  looked  to,  as  in 
many  positions  (130,  a)  it  may  lead  to  faulty  progressions: 

a.  h.      _  C. 


t 


whereas,  in  the  position  at  b  and  c  the  third  has  more 


freedom. 


Remark.— The  natural  progression  of  this  chord  to  the  tonic,  as  well  as  of  that  on 
the  seventh  degree  in  major,  led  the  older  theorists  to  regard  the  dominant  as  the  funda- 
mental basis  of  the  chord.  They  conceived  it  to  be  a  chord  of  the  dominant  seventh 
with  an  added  ninth — major  or  minor — and  with  the  fundamental  omitted,  thus  form- 
ing both  chords  of  the  seventh  degree.  In  referring  to  what  is  said  later  (Chap.  IX), 
of  the  chord  of  the  ninth,  we  need  only  state  here  as  a  reason  for  the  view  offered 
that  this  assumption  of  the  chord  of  the  ninth  is  needless  and  far-fetched,  and  that 
simplicity,  for  practical  purposes,  is  preferable  to  any  complicated  theoretical 
explanation. 

In  the  application  of  the  chord  of  the  diminished  seventh,  observe 
the  following : 

The  diminished  seventh,  the  least  harsh  of  all  the  secondary  sev- 
enths, needs  ?to  preparation. 

Exercises. 


gg 


7 

5J 


62        6 


6  7 

4  i 


^£=1= 


86 


MANUAL  OF  HARMONY. 


^m 


7   6^ 

*  4      2 


7 

7         8 

&- 


a 


:«^-« 


i=f 


Sisf^ 


*  •  .,L^-J_^ 


6  7 

6  4  $ 


e^ii 


-\=± 


6 

4          7 


7 
6  $ 


7 

7        { 


§*3 


g?=^ 


I 


44=4: 


t=^ 


-■^H-ti^ — '^- 


Ute^i 


53f        7 


il 


4H        gj      =^ «'-F^ 5=   (^         -4—  =3 


7.         8  7 


6 

J  5 


g%=p= 


^^=S? 


-F^ — d- 


?i==t 


us 


6         7  X 


ISE^iS 


7 
7          X 


:i;i 


^==s: 


^^=f= 


These  and  all  former  exercises  in  this  chapter,  the  object  of  which 
was  only  to  assist  us  in  learning  the  mechanical  use  of  the  chords  and 
to  test  the  rules  and  remarks,  have  something  hard  and  inflexible  in 
their  structure,  since  the  great  number  of  seventh  chords  here  were 
only  possible  in  their  fundajnetital  positions.^  and  because  the  intro- 
duction of  many  of  them,  from  our  present  standpoint,  which  did  not 
allow  us  to  select  other  means,  was  difficult  and  could  only  seem 
forced.      The  following  may  help  to  explain  them  : 

The  fundamental  of  these  chords  of  the  seventh  move  everywhere 
by  skips  of  a  fourth  or  ffth^  as  the  bass  parts  show.  Only,  in  the 
third  exercise  of  Nos.  122  and  131,  there  seems  to  be  an  exception. 
In  the  fourth  measure  of  the  third  exercise  of  No.  122  the  bass  tone 
remains  stationary  (on  a),  but  the  regular  fundamental  progression 
is  maintained  in  the  two  chords  according  to  rule  :  ^7,  D7:  The  bass 
tone  could  be  sustained  here,  as  we  have  already  learned  how  to  use 


MANUAL  OF  HARMONY.  87 

the  inversions  of  the  chord  of  the  dominant  seventh.  The  case  is  the 
same  in  the  third  exercise  of  No.  131,  where  the  fundamental  pro- 
gression is  A^ — d^  on  the  sustained  A  of  the  bass. 

In  the  second  example  of  No.  131,  the  chord  of  the  seventh  on  the 
third  degree  in  minor  is  introduced.  It  is  strictly  prepared,  and  on 
that  account  w^ill  not  appear  harsh  or  unnatural. 


CHAPTER   VII. 

INVERSIONS    OF    THE    SECONDARY    CHORDS    OF    THE    SEVENTH. 

The  inversions  of  the  secondary  chords  of  the  seventh  in  major  or 
minor  give  the  same  derived  chords,  as  those  of  the  dominant  sev- 
enth, namely  :  the  chord  of  the  sixth  and  fifth,  of  the  sixth,  fourth 
and  third,  and  of  the  second.  The  differences  in  the  thirds,  fifths 
and  sevenths  in  the  fundamental  chords  will  require  no  alteration  in 
the  treatment  of  the  inversions.  Notwithstanding  that  the  major 
seventh  is  changed  by  inversion  into  a  minor  second,  and  the  dimin- 
ished intervals  into  augmented,  yet  their  progression  takes  place  in 
the  same  manner  already  described. 


No  new  rules  are  required  for  the  resolution  of  these  chords,  only 
in  the  resolution  of  the  inversions  of  the  chord  of  the  seventh  on  the 
seventh  degree,  care  is  necessary,  as  was  said  before,  to  avoid  the 
parallel  fifths  which  creep  in  so  easily. 

This  may  be  added  here : 

Progression  of  the  Chord  of  the  Seventh  Degree  in  Major. 


183. 


88  MANUAL    OF  HARMONY. 

All  the  above  inversions  are  good.  That  of  the  cliord  of  the  sec- 
ond., however,  is  less  used,  as  its  resolution  is  to  the  chord  of  the  sixth 
and  fourth,  which  can  seldom  be  used  but  as  a  passing  chord.  We 
should  not  be  misled  by  the  compact  form  of  these  chords  in  No.  133 
as  to  their  usefulness.  The  only  important  point,  as  mentioned  before, 
is  whether  the  seventh  appears  above  or  beloiv  the  fundamental. 
Positions  of  the  chords  of  the  sixth  and  fifth  and  of  the  fourth  and 
third,  like  the  following  : 


are  more  satisfactory,  because  the  seventh  is  heard  above  the  funda- 
mental. The  chord  of  the  diminished  seventh  requires  a  resolution 
similar  to  the  above,  e.  g. 

6 


V1107 1 


The  third  inversion,  the  chord  of  the  second,  will  here  also  be  the 
least  satisfactory,  on  account  of  its  resolution  into  the  chord  of  the 
sixth  and  fourth,  a  chord  which  requires  most  careful  treatment.  The 
parallel  fifths  which  appear  in  the  resolution  of  the  chord  of  the  sixth 
and  fifth,  and  of  the  fourth  and  third,  like  those  below,  are  consid- 
ered faulty,  as  was  said  before,  e.  g. 


fe'.L-^i— =fe:^£ 


i^ 


With  this  very  pliable  chord,  the  position  of  the  fundamental  in 
regard  to  the  seventh,  makes  no  such  material  difference  as  is  the 
case  with  the  chord  of  the  seventh  on  the  seventh  degree  in  major. 


MANUAL  OF  HARMONY. 


89 


Whether  the  seventh  \\q.%  above  or  below  the  fundamental,  the  siniihir- 
ity  of  sound  between  the  augmented  second  and  tlie  minor  third  always 
softens  the  chord,  and  causes  the  former  to  be  felt  as  such  only  in 
respect  of  the  key. 

Exercises. 


37.^§^|^|| 


^=i 


4 
.3       7. 


§J^JEEgE^pEEgE§E3:^t=f=P=F=F^p=^^^ 


:t^ 


-f=^= 


2 


6 
6        6 


^^=t 


i 


M 


6 

5         2 


4 
7  3      6 


6 
6         6 


^fE^=^^^^ 


^ g> p2 


iS* P' SI 


Bife 

3         2 

6 

t- 

6 

6 

2 

6 

6 
5 

(^ 

7 

7 

— ^H 

--C — \\i— 

r^- 

-L- 

tf- 

-<&- 

L-t= 

t^Z 

-M 

t^ 

§3E 


^F==t 


-« — ^ 


0 

4  6 

6  7  7         3  6  5  Jt 


;tt± 


z^ s> g 


f==t 


a 


aii^^feS^ 


6 

5       J 


F 


E3 


-^ — ^2- 

1=1= 


I 


90 


MANUAL    OF  HARMONY. 


ga!>"TrTT^giEg£=5 


7  6      6  7 

«  4     4  « 


I 


10. 


^» 


4 
7  3     J 


^^ 


6 
6      4 


E#=E^ 


I 


CHAPTER  VIII. 

THE  CONNECTION  OF  THE  CHORDS  OF  THE  SEVENTH  WITH  CHORDS 
OF  OTHER  DEGREES  NOT  YET  USED. 

The  rule  that  the  seventh  must  d/e^ce?zfl^  one  degree,  is,  indeed,  justi- 
fied in  the  chord-connections  previously  shown,  but  it  has  as  little 
positive  authority  as  anything  else  which  is  subject  to  the  necessary 
changes  which  occur  in  the  great  variety  of  chord-connections. 

The  progression  of  the  seventh.^  or  its  inversion,  the  second.,  de- 
pends entirely  on  that  of  \\\q  fundamental.  If  this  is  in  such  a  way 
that  a  satisfactory  and  intelligible  effect  is  only  possible  through  a 
descent  of  the  seventh,  then  the  above  rule  will  hold  good. 

The  progression  of  the  fundamental  may,  however,  be  such  that 
the  seventh  shall  remain  statio?iary  or  even  ascend^  e.  g. 


13S. 


h=A 


-7^- 


The  above  example  shows  the  possibility  of  connecting  the  chords 
of  the  seventh  with  other  chords  than  those  hitherto  employed. 

A  few  known  kinds  of  chord-connections  will  follow  with  remarks, 
that  we  may  be  able  in  forming  new  ones,  to  proceed  in  accordance 
with  criticial  principles. 

We  begin  with  the  chord  of  the  dominant  seventh. 

The  resolution  of  the  choixls  of  the  seventh  according  to  previous 
rules  was  called  cadence,  and  that  of  the  chord  of  the  dominant 
seventh  the  closing  cadence. 


MANUAL  OF  HARMONY.  _  9 1 

When  the  chord  of  the  dominant  seventh  is  followed  by  a  chord 
ether  tha?t  the  tonic  triads  the  fiatural  tendency  to  a  close  is  either 
delayed  or  destroyed  altogether.  Thus,  the  feeling,  or  anticipation 
of  the  natural  resolution  experiences  a  disappointment;  hence  these 
unexpected  resolutions  are  called  deceptive  cadences  (false  cadence). 

Some  methods  of  making  these  cadences  follow  : 

I.  The  cofinectio7i  of  the  chord  of  the  dojninant  seventh  with 
triads  other  than  the  tonic,  the  seventh  descending  by  a  degree. 

a.  Connection  with  the  sixth  degree. 


In  major 


139 


C:  V7       VI       '^ " a:  V7       VI  

This  progression  (deceptive  cadence)    is  very  often  used. 
The  effect  of  the  inversions  of  the  chord  of  the  seventh  is  less  de- 
cided than   in  the  fundamental  position;   they  are  therefore  seldom 
used. 

In  major, 
6  6 

J>  -'^ 


C:  V7        VI  

b.   Connection  with  the  third  degree. 


Better  position. 
7  6 


s^=l^^=l^^] 


a:  V7 


VI 


C:  V7 


Remark.— The   inversions  of  the  chord   are  omitted   here.     They  can  easily  be 
made. 

This    progression    becomes    still  more  effective    if    a    modulation- 
towards  a  minor  be  introduced  : 


142. 


92 


MANUAL  OF  HARMONY. 


A  connection  with  the  triad  on  the  third  degree  in  minor  can  also 
be  made.  The  latter  chord,  however,  being  also  a  dissonance,  on 
account  of  its  augmented  fifth,  will  also  require  a  resolution. 


-fe- 


11^^ 


3&: 


I 


a:  V7       111'      VI 


2.    Conitection  with  triads^  while  the  sevetith  remaiiis  stationary, 
a.     With  the  second  degree. 


Not. 


Not  good  in  minor. 


14-4. 


W- 


^ 


^=i^Ea^:l 


C:  V7 


b.     With  the  fourth  degree. 


In  major 


a:  V7       11° 


6 

■'5' &- 


-I       g>^s? — I 


^ 


c^        _^_  

-rr     -<^'            -7:3-     -<5>- 
C:  V7     IV  a:  V7     IV  

Connection  of  the  chord  of  dominant  seventh  with  other  chords  of 
the  seventh  besides  those  already  used,  is  possible.  A  few  here 
follow : 

Sixth  degree.  Third  degree.         Or.  Minor.        Third  degree. 


1 46.  f  fes=i=M=M=^=M- 


&^! 


t 


Z/-  -27- 

C\  V7      V17 


-Z7- 

V7 


-ST 
III7 


V7  cv.  V7 


</:V7        ni'7     VI 


If  modulations  are  introduced,  many  new  connections  of  chords  of 
the  seventh  become  possible,  e.  g. 
a.     With  seventh  descending. 


147. 


;^: 


fci^iii^ig^iiii^^ 


C:  V7     d:  V7 


C:  V7  /':  VI1O7  a:  V7     /^:  V7  a:  V7   (7:  VII© 


MANUAL    OF  HARMONY. 
b.     The  seventh  stationary. 


93 


C:  VlE^:  V7  C:  ViB^i  V7  a:  V7  C:  V7  a:  V7   G:  V7 


3.      Connection  of  the  chords  tvii/i  the  seventh  ascending. 
This  may  occur  in  the  regular  cadence  progression,  V7 — I,  117 — V, 
or  whenever  the  fundamentals  progress  by  the  usual  cadence  step. 
a.     By  an  exchange  of  voices  in  their  progression. 


lij^ii^giFi^g:^^^^^:! 


;H 


When  the  fcnda?nental  oi  a  seventh  chord  skips  dozvjizvard  a  third, 
the  resolution  of  the  seventh  downward  a  degree  is  impossible  on 
account  of  the  faulty  covered  octaves  which  result,  e.  g. 


m^^ 


150. 


^0 


This  progression  cannot  be  used  in  the  other  voices; 


p^^ 


1 


^^^^m 


I 


The  above  examples  are  all  faulty. 


94 


MANUAL  OF  HARMONY. 

b.     The  fundamental  lone  remaining  stationary  : 

Not. 


In  this  case,  the  seventh  must  lie  at  a  distattce  from  the  funda- 
mental ;   the  following  progression  is  therefore  faulty : 


By  chromatic  alteration  and  modulation  : 

I  4  6  if 

7  3  7  3  5  2 


•^Ji 


T^^- 


^i 


^-- 


-z?^- 


C:  V,   (7:  V, 


i 


Enharmonic.     $ 
7  3 


z?^ 


4£ 


^EEl 


i— ^— p: 


@ 


C:  V7C:  V7  V7  e:  YuO^  C:  V7  F1,^:V^ 

d.     By  contrary  motion  of  the  bass  and  modulation  into  other  keys  : 


155. 


^«: 


C:  V7  ./:  V7  C:   V7  /'b:  VI1O7 


V7  (1:  VI1O7 


C:  V7  F:  V7 


The  foregoing  examples  of  chord-connections  give  only  an  intima- 
tion of  the  possible  combinations.  Their  object  was  to  draw  atten- 
tion to  the  great  variety  of  harmonic  progression,  and  its  adapta- 
bility for  composition. 

Criticism  only  can  decide  as  to  the  value  of  these  and  similar  com- 


MAt^UAL  OF  HARMONY. 


95 


binations,  since  their  proper  use  is  only  possible  by  considering  their 
introduction,  progression,  rhytJiniical  -weight,  and,  in  fact,  their 
whole  situation. 

The  character  of  a  piece,  the  movement  of  the  voices  with  reference 
to  a  theme  or  an  idea,  or  similiar  causes,  may  lead  to  such  harmonic 
combinations.  To  apply  them  at  random,  how^ever,  for  the  sake  of 
appearing  original,  would  so  seldom  succeed  that  the  object  would 
hardly  be  recognized. 


Exercises. 


156. 


•^§±E$i 


1==t 


-5*— <S- 


^ (2- 


I 


4        6 
6        3,       4 


Sa 


t^ 


^=t 


1=::^ 


Hfj 


f^ — 6^ — zg^ 


SiE^ 


6 
4  7 


6 
2  6 


■^=? 


G> |g g -gj 61- 


3*0: 


6         6  6 

5        6       6         6  7        6         5 


^ ^- 


-G>—^ 


m^^^^ 


5.       Open       4 

position.  3         6         6  7 


a 


i^^l^p^ 


6  5        - 


6   7 

4  « 


gS=i 


6  7 

4^6         % 


^^ 


6  6       4  6   7 

6  ,6  43  66,4$ 


ila^ 


z?- 


n 


S^i 


6        6 
6        6 


6 

47 


H 


Remark. — The  open  position  in  the  5th  exercise  above,  has  reference  to  a  move- 
ment of  the  voices  shown  at  Ex.  152. 


96 


MANUAL    OF  HARMONY. 


Connection  of  the  Secondary  Chords  of  the  Seventh  with  other 
Chords  of  Various  Degrees  or  Keys. 

It  would  be  impossible  as  well  as  unneccessary  to  give  examples  of 
all  the  comiections  o£  the  secondary  chords  of  the  seventh  with  other 
chords.  A  few  more  connections  of  chords  with  secondary  chords 
of  the  seventh  may,  however,  follow  here. 

a.       With  regular  progressio7t  of  the  seventh. 


b.       With  free  progression  of  the  seventh. 


S 


1 58.  i: 


--^-. 


viZL^rzz:^^ 


C:n1   G:Vr 


S5~ 


* 


'-Wr 


Remark.— The  reason  why  the  last  example  is  not  good,  lies  in  the  so-called  cross 
relation,  an  explanation  of  which  follows  later. 


59. 


The  last  progression  above  is  much  used.  The  cadencing  progres- 
sion (II — V)  is  delayed  by  inserting  the  chord  of  the  sixth  and 
fourth  of  the  tonic  between  them.  The  chord  of  the  sixth  also  often 
appears  between  the  seventh  chord  and  its  resolution,  as  in  example  c. 

The  chord  of  the  di7ninished  seventh  is  often  resolved  in  the  same 
manner : 


MANUAL    OF  HARMONY. 


97 


g,  viio^    C:  I  V  -  c. 

The  natural  progression  is  here  also  only  delayed  by  the  use  of  the 
chord  of  the  sixth  and  fourth. 

The  mechanical  combination  of  such  progressions  of  chords  may  be 
left  to  personal  practice  and  examination.  The  advantages  to  be  de- 
rived from  it  vs'ill  be  found  in  the  insight  which  is  gained  of  the  rela- 
tionship of  chords,  and  therefore  should  not  be  too  lightly  esteemed. 
This  practice  will  stand  in  about  the  same  relation  to  composition 
itself,  as  technical  studies  and  exercises  do  to  the  practical  representa- 
tion of  musical  works.  Both  produce  readiness  and  skill,  develop 
the  powers,  and  make  possible  meritorious  productions. 

It  may  still  be  I'emarked  in  addition,  that  the  I'elation  of  the  seventh 
to  the  fundamental  and  its  progression  will  always  be  regarded  as  the 
test  of  the  above  combinations.  If  this  is  pure  and  the  other  voices 
contain  none  of  the  faults  before  mentioned,  the  chord  connection 
may  be  used  for  particular  cases. 

Exercises. 


161 


■•Ei±$: 


gaSE^s 


t=|: 


t^t 


4        7 
6       7   3        5    6     2 


7  6       6 

5      6     4       6 


"^^^i^j^^^^E^^^Em^^t^^x 


5       4         7         7        7 


§a$^ 


6         6        7        4        7 

-a ^^_ 


v=t 


t=^-=^^ 


98 


MANUAL  OF  HARMONY. 


§±f; 


6         6 


6         67 


1 


6$     6 


$        6 
6       4 


6  7 

4  $ 


x==x 


s 


Sii^ 


^ 


:^tt* 


1* 


EP 


f     2 


^ 


87 

6      » 


-^-M^ 


1    M       I    L[ 


EEi! 


feTEE 


:§Sffi^ 


6  7 
43f 


=#^ 


1: 


1 


Remark. — Many  of  the  cases  cited  above  were  not  included  in  these  exercises,  as 
they  are  based  upon  modulation,  which  is  not  fully  explained  until  later.  (The  sixth, 
exercise,  second  measure,  has  an  application  of  modulation.)  Many  of  the  above  exer- 
cises would  have  been  smoother  and  more  melodious  by  the  application  of  modulation^ 


CHAPTER   IX. 


CHORDS    OF    THE    NINTH,    ELEVENTH    AND    THIRTEENTH. 

Lengthy  discussions  respecting  these  chord-formations  are  found  in 
most  text-books. 

The  views  which  may  be  entertained  respecting  these  chords  are 
various,  but  they  all  tend  to  one  practical  result.  It  may  be  taken  for 
granted  that  these  are  either  real  chords,  such  as  the  chord  of  the 
seventh,  in  which  case  they  must  be  considered  and  treated  as  such, 
or  else  they  belong  to  the  list  of  suspensions,  or  occur  accidentally 
when  one  or  more  parts  remain  stationary. 

In  the  first  case  their  explanation,  and  especially  that  of  their  inver- 
sions, would  be  extremely  prolix,  and  moreover  the  chords  them- 
selves would  often  be  difficult  to  recognize,  inasmuch  as  in  four-part 


MANUAL  OF  HARMONY. 


99 


harmony  one  or  more  of  their  intervals  must  always  be  omitted.  If, 
however,  they  are  considered  as  suspensions  or  accidental  chords, 
their  explanation  becomes  very  simple. 

Remark. — The  chords  of  the  ninth,  eleventh,  etc.,  are  but  a  relic  of  the  old  systems 
of  thorough-bass,  so-called,  in  which  every  combination,  no  matter  how  transitory  or 
accidental,  was  usually  treated  and  taught  as  a  fundamental  harmony,  the  consequence 
ot  which  was  to  render  the  study  of  the  theory  of  music  much  more  complicated  and 
difficult. 

While  being  unable  here  to  go  further  into  the  theoretic  reasons  for 
classifying  these  formations  as  accidental  ones,  the  possibility  of  sim- 
plifying the  harmonic  system  without  real  practical  disadvantage  has 
determined  us  to  take  the  latter  view.  (More  upon  this  subject  in 
Part  II.) 

In  order  to  obtain  a  clear  insight  into  their  nature,  we  will  show 
the  formation  of  these  unessential  chords,  and  add  some  remarks. 

By  adding  to  the  chord  of  the  dominant  seventh  another  third  dis- 
tant a  ninth  above  the  fundamental,  a  chord  is  formed  which  is  known 
as  the  chord  of  the  dominant  ninth. 

In  the  major  scale  the  ninth  will  be  jiiajoi-^  and  in  the  minor  scale 
minor  : 


In  minor. 

— ^ 

I — J" &< 

162. 


M 


In  strict  harmonic  progression  it  is  necessary  that  either  the  ninth 
or  the  fundamental  should  be  prepared,  as  in  the  case  of  the  domi- 
nant seventh.  The  following  example,  therefore,  in  which  both  fun- 
damental and  ninth  enter  free^  is  objectionable  on  account  of  the 
stiffness  and  lack  of  connection. 


163.< 

\  -&-  -G- 


MANUAL    OF  HARMONY. 


The  preparation  may  take  place  as  follows : 


164. 


In  what  respect  the  first  examples  are  to  be  regarded  as  suspensions, 
and  the  last  as  accidental  combinations,  will  be  seen  in  Part  II. 

Remark. — From  the  chord  of  the  ninth  in  major  they  derive  the  chord  of  the  sev- 
enth on  the  seventh  degree,  which  has  been  already  fully  treated,  also  the  chord  of 
the  diminished  seventh  from  the  chord  of  the  ninth  in  minor,  in  order  to  be  able  to 
form  their  cadencing  progression  in  a  manner  similar  to  the  other  chords  of  the  sev- 
enth, asserting  that  these  chords  are  themselves  chords  of  the  dominant  seventh  with 
the  ninth  added  and  the  fundamental  omitted,  e.  g. 


In  the  first  instance  arises  the  difficulty,  that  we  must  accept  two  chords  of  the  sev- 
enth degree  in  major — one,  whose  natural  cadence  is  the  following: 


i 


and  the  other  as  derived  from  the  chord  of  the  dominant  seventh.     It  seems  that  the 
clearest  way  is  to  refer  to  the  leading  tone  upon  which  these  chords  are  built. 

Many  theoretical  works  treat  also  of  the  formation  of  other  chords 
of  the  ninth,  called  secondary  chords  of  the  ninth ;  this  is,  however, 
quite  unnecessary,  for  inasmuch  as  they  can  never  appear  without 
preparation,  their  treatment,  resolution,  etc.,  will  be  in  every  respect 
similar  to  that  of  suspensions. 

That  which  applies  to  chords  of  the  ninth,  will  apply  in  a  greater 
degree  to  chords  of  the  eleventh  and  thirteenth,  which  are  still  less 
worthy  to  be  regarded  as  real  chords. 


MANUAL  OF  HARMONY. 


These  formidable  looking  chords  are  as  follows: 


167. 


1  3 

1  1 


It  is  evident  that  they  can  never  be  employed  in  pure  four-part 
writing,  since  the  necessary  omission  of  some  of  their  intervals  would 
completely  alter  their  nature,  and  transform  them  into  simple  suspen- 
sions, thus  : 


168. 


i 


±=F= 


^ 


^m 


:i^i^ 


And  even  in  compositions  with  more  than  four  voices,  where  they 
might  appear  in  their  complete  form,  their  character  and  treatment 
will  still  be  that  of  suspensions,  while  in  the  more  free  style,  where 
they  may  also  occur  without  preparation,  they  can  be  regarded  as 
■changing  or  auxiliary  notes. 


CHAPTER.  X. 


CHROMATIC    ALTERATION    OF     FUNDAMENTAL     HARMONIES  ; 
ALTERED    CHORDS. 

The  chromatic  alteration  of  one  or  more  intervals  of  a  fundamental 
chord  produces  one  of  two  different  effects :  it  either  causes  a  modu- 
lation into  some  new  key,  or,  it  gives  an  entirely  new  form  and  con- 
struction to  the  chord  itself.  If,  for  example,  the  major  triad  be 
chromatically  altered  in  the  following  manner,  there  will  arise : 

a.     Modulations. 


a..^§Ej=^=^^g;Ep^°|^^^^ 


I03 


TylANUAL    OF  HARMONY. 


Through  C^,  the  diminished  triad  of  the  seventh  degree  in  D  major 
or  d  minor,  or  of  the  second  degree  in  b  minor; 

Through  El?,  the  c  minor  triad ; 

Through  Ej?  and  Gb,  the  diminished  triad  of  the  seventh  degree  of 
DI2  major  or  minor,  or  of  the  second  degree  of  b\>  minor. 

The  last  X^no  alterations  are  only  transpositiotis  of  the  same  chord 
into  other  keys,  namely,  C^  major  and  C^  major. 

b.     New  forms. 


,70.  pt^E^p^^^1^f^|^«^H 


Of  these,  the  formations  at  a,  b,  d,  f,  can  occur  accidentally  by  the 
means  of  passing  tones,  but  they  have  no  harmonic  value. 

It  is  different  with  those  at  c  and  e,  which  have  the  character  of  real 
chords. 

The  first  form  of  the  triad  {c)  is  known  as  the  augmented  triad. 
This  chord  was  first  found  on  the  third  degree  of  the  minor  scale.  As 
before  mentioned,  it  seldom  appears  in  this  connection,  but  more  fre- 
quently as  triad  on  thtjirst,  fourth  Sindjifth  degrees  in  major,  with 
its  fifth  raised  chromatically.  It  is  easy  of  explanation,  as  the  pass- 
ing tone  (G||)  to  the  following  note  (A)  and  its  progression  is  in- 
cated  by  this  tone  (Gj:|)  as  an  augmented  interval : 


SEEg- 


r-§- 


The  inversions  of  this  chord  are  also  practicable 


li^lilili^lH 


IV 


Although  these  chords  are  generally  used  either  as  passing  chords, 
or  with  the  fifth  prepared,  yet  in  rapid  changes  of  harmony  they  may 
also  enter  free,  that  is,  without  preparation  : 


MANUAL  OF  HARMONY. 


[03 


173. 


i-,LiJ 


^S^^ 


9fc 


I 


To  the  augmented  triads  on  the  first,  fourth  and  fifth  degrees  may 
be  added  the  sevenths  belonging  to  those  degrees.  The  chord  of  the 
dominant  seventh  is  the  one  most  used. 

a.      The  augrmented  triad  in  connection  with  the  dominant  seventh. 


1  74. 


4  4 

3        6        3        6 


S       X 

2       6       2        6 


^=^^^^^^m 


^'^^  ,^Z|7_^^2_|_^_^|ig^ 


^i^ 


C:     V7     I  - 

6.      In  connection  with  the  seventh  of  the  first  degree 

ft 


.-^ 


^S> 5;: 


_^_ ^     -^- ^_ 


\^^^3^E^^p^J3^E^=S--J^^-=^f^^ 


C:     Irr.    IV 


c.     The  addition   of   the   seventh   to   the   augmented   triad   of  the 
fourth  degree  is  very  seldom  used. 


4  4 

3  6  2  6 


—''-^  eJ — H 


176.< 


_-gl 


-to: 


-f5> a.- 


I 


C:     IV7,    viio 


I04 


MANUAL   OF  HARMONY. 


In  all  the  above  examples  the  ordinary  cadencing  progression  of 
the  fundamental  has  been  adopted.  The  following  examples  will 
serve  to  show  that  the  chords  of  the  seventh  with  the  augmented  fifth 
can  also  be  used  with  other  chords  of  various  degrees  and  in  different 
keys,  and  with  different  bass  progressions. 


==l^fetl 


C:  V7     e:  V7 


C:  III 


l7.    d:  V         C:   ill 


I7.    G:   V7 


These  harmonic  combinations  which  occasionally  sound  so  unusual 
and  harsh  acquire  importance  only  through  their  connection  with 
other  chords,  and  especially  if  in  a  certain  degree  they  are  brought  about 
through  an  inner  necessity  of  the  voice-leading. 

If  it  is  the  duty  of  a  text-book  to  show  the  possibility  of  such  har- 
monic combinations,  it  is  also  its  duty  to  caution  the  Student  against 
employing  them  until  he  is  thoroughly  conversant  with  the  simpler 
and  more  important  forms  of  harmonic  progression. 

Exercises. 


MANUAL    OF  HARMONY. 


105 


6  6S 
6  4 
3  2     6 


aa 


6 
4  7 


II 


4.         6 

3»,  li 

6 

N.I 

3  6$ 

6             6 

6 

II 

[')•#/* 

^             1 

1              1 

/J 

11 

y  T  \\j 

"1             ^ 

(d        ^ 

11 

' 

Lfii 1 

L_s'_IJ 

gifrp=r 


iS 


6  $ 
4  — 
2    — 

25- 


I 


6P 


7  6 
5  5 


6 

45  Q 


a_%ia3 


H 


eq 

4  4 

2         6       3 


35tef?^E 


a2¥ 


6        6 
4        5 


:1=P 


■^zf^zi^ 


:^ 


aaSE^^ 


^==1= 


^ 


6         4    6$ 


ii 


6- 
5- 

t 


§-%* 


1=i=t 


IB 


e 


^ 


In  the  fourth  exercise  at  N.  B.,  the  fifth  of  the  minor  triad  on  the 
second  degree  is  augmented.  The  effect  of  this  unusual  combination 
is  not  unpleasant  in  its  present  position.  From  this  it  will  be  seen 
that  the  natural  progression  of  parts  will  often  lead  to  new  combina- 


io6 


MANUAL    OF  1/ A  R  MO  NY. 


tions,  which,  however,  are  not  of  sufficient  importance  to  require  sep- 
arate consideration. 

Note.— In  the  fifth  measure  of  No.  i   in  the  above  exercises,  a  sign  occurs  which 

has  not  been  used  before  ;  this  is  the  horizontal  line, ,  which  being  placed  after  a 

figure  indicates  that  the  interval  is  to  be  sustained. 

To  illustrate  the  proper  manner  of  working  out  these  exercises,  the  first  example 
above  is  here  given: 


:]==t 


S5 


xig: 


6$ 


H      3 


m 


-^ 


Ed. 


^ 


C:  I •       IV II  viiO     I  V?- 


I      117     V 


From  the  formation  at  e  of  example  1 70 : 


(which  is  also 


known  as  the  double-diminished  triad)  arises  a  chord  which  is  often 
used,  namely :  the  chord  of  the  augmented  sixth. 
The  first  inversion  of  this  chord  gives : 


feiii^ 


P^: 


W 


Its  resolution  (as  at  b)  is  determined  by  the  rule  that  augmented 
intervals  must  ascend.  This  chord  is  naturally  resolved  into  the  chord 
of  the  dominant,  as  in  179,  where  the  chord  of  the  augmented  sixth, 
which  is  derived  from  the  minor  triad  on  the  fotirth  degree  of  the 
scale  of  g  minor.,  is  resolved  into  the  triad  of  the  fifth  degree. 

NoTK.  —  The  natural  tendency  of  the  subdominattt  triad  is  to  pass  into  that  of  the 
dominant.  When  its  fundamental  is  raised.a  chromatic  half-step,  and  the  chord  in- 
verted, the  pressure  towards  the  dominant  is  very  much  increased  by  the  direction 
which  the  altered  interval  fnust  take.  —  Ed. 

The  chord  of  the  augmented  sixth  is  peculiar,  from  the  fact  that 
its  third  (original  fifth)  only  can  be  doubled  in  four-voiced  writing. 


MANUAL   OF  HARMONY. 


107 


180. < 


i^^i^iiB 


:&g: 


:b 


The  other  positions  of  the  original  chord  (tlie  so-called  donhle-dim- 
inished  triad)  are  also  available.  The  second  inversion  (|)  can  be 
used  in  four  parts  when  the  voices  lie  in  a  very  open  position.  The 
fundamental  position  can  be  used  in  three  parts,  but  seldom  occurs. 


181. 


1- 


d22: 


=f:^^ 


h.  Not 


1^ 


m^B^^m 


Remark. — The  chromatic  alteration  of  an  interval  of  the  minor  triad  is  already 
shown  in  the  formations  at  169  and  17c,  and  needs  no  further  investigation.  Also, 
the  chromatic  alteration  of  an  interval  of  the  diminished  triad  will  result  in  either 
a  major  or  minor  triad,  or  formations  already  contained  in  the  examples  referred  to 
above. 

Thus,  the  form  of  the  triad  in  No.  170,  d,  will  be  like  the  following  which  belongs  to 
C  major: 

Better  in  open  position. 


i 


K 


I 


C\  vuo 


In  many  text-books  this  chord  is  termed  the  harsh  diminished  triad.  Such  chords 
appear  only  incidentally,  in  passing,  and  their  progression  is  determined  by  their 
intervals  —  the  augmented  ascending  a  degree,  the  diminished  descending  a  degree. 


T/ie  chrotnatic  alteration  of  an  interval  of  the  chord  of  the  seventh, 
has  already  been  noticed  (page  103),  where  the  chord  of  the  seventh 
was  found  combined  with  the  augmented  triad.  Of  the  other  second- 
ary chords  of  the  seventh,  that  on  Xhesecofzd  degree  oj"  the  minor  scale 
is  of  especial  importance  among  the  altered  chords  which  in  the  fol- 
lowing form  produces  chords  very  much  used. 


Io8  MANUAL    OF  HARMONY. 

By  chromatically  raising  the  third: 


183. 


* 


I1O7 


If 


the  following  inversions  are  given 


184. 


"# 


*■ 


Of  these,  the  second  inversion  is  most  used ;  the  others  appear  very 
rarely. 

This  chord  in  its  second  inversion  is  known  as  the  chord  of  the 
augmented  sixth,  fourth  and  third. 

Its  resolution  is  founded  on  that  of  the  fundamental  chord ;  thus, 
as  the  chord  of  the  seventh  on  the  second  degree  resolves  naturally 
into  the  dominant,  this  will  also  be  the  case  with  the  altered  chord 
and  its  inversions : 


3^ 


-fe- 


^ 


-~sr- 


I 


a:  IIO7 


If  the  fundamental  be  omitted  in  this  chord,  we  have  the  augmented 
sixth  chord,  shown  above,  thus  explaining  the  natural  tendency  of  the 
chord  to  the  dominant : 


^^E 


With  omission  of 
the  fundamental. 


a:  I1O7 


* 


a:  I1O7    V 


or  compared  with  No.  179,  in  G  minor  : 
•"undament 


Fundamental  chord.    Chro.  raising 
of  the  third. 


Aug.  chord  of  the  sixth,      Aug.  chord  of 
the  sixth. 


burth  and  third. 


:^i= 


^1107 


it 


«^ 


g-.  1107 


fe 


=«§= 


1107 


MANUAL  OF  HARMONY. 


[09 


Remark. — It  may  be  further  remarked  that  the  chord  of  the  augmented  sixth, 
fourth  and  third  can  also  be  formed  by  adding  a  seventh  to  the  harsh  diminished  triad, 
mentioned  on  page  107.  The  resolution  would  be  different,  however,  as  Ma/ chord 
was  found  to  rest  on  the  seventh  degree,  while  this  rests  on  the  second. 

Instead  of  the  fundamental,  the  ninth  of  the  original  chord  can  be 
added,  whence  is  formed  the  chord  of  the  augmented  sixth  and  fifth. 

It  is  formed  as  follows  : 


Fundamental 
chord. 


Without  fundamental,    Inversions. 
With  ninth.      with  elevation        a         $  h 

of  the  third.  '        5 


•^iE^=i=E^^i^ 


S&7 


w 


m^m 


Of  these  chords,  the  ^rst  inversion  (a)  is  the  most  practicable. 
The  other  inversions  are  seldom  used. 

Its  natural  resolution  is  again  the  same  as  that  of  the  already  men- 
tioned nearly  related  chords,  namely,  to  the  dominant,  but  the  direct 
resolution  always  causes  parallel  fifths. 


-■^^^^^m 


These  fifths,  which  are  not  among  the  most  objectional  ones,  may 
be  avoided  in  three  ways ;  firstly,  by  an  anticipated  resohction  of  the 
fifth  (the  original,  above-inentioned  ninth  as  a  supension),  as  in  Ex. 
190  at  «;  secondly,  by  a  free  progression  of  the  fifth  to  the  third  of 
the  same  chord,  as  at  b ;  and  thirdly,  by  delaying  the  resolution  of 
both  third  and  fifth,  whereby  the  chord  of  the  sixth  and  fourth  is  in- 
troduced between  the  augmented  chord  of  the  sixth  and  fifth  and  its 
resolution,  as  at  c.  The  latter  method  is  the  one  most  frequently 
used. 


•i^H^lfc^Si^fe 


Not. 

I 


Better. 

I 
-G>- 


Ete 


=g=±=i=l=g_l^^-F5^4r-^rfEH 


■fe 


Note.— The  above  three  chords  may  be  used  in  major  as  well  as  minor,  as  the 
dominant  harmony,  into  which  they  all  resolve,  is  the  same  in  both. — Ed. 


,IO  MANUAL  OF  HARMONY. 

Remark. — The  addition  of  a  ninth  is  not  sufificient  to  warrant  us  in  classing  this 
harmony  as  a  chord  of  the  ninth.  .  The  progression  at  a  shows  very  clearly  that  the 
ninth  has  here,  as  elsewhere,  the  character  of  a  suspension,  and  the  same  may  be 
said  of  the  progressions  at  b  and  <r,  which  are  treated  precisely  like  suspensions,  in 
so  far  as  they  require  preparation.  It  would  seem  from  this,  that  this  harmony  should 
have  been  treated  in  connection  with  the  suspensions.  As  the  question  of  origin  was 
under  investigation,  however,  it  was  proper  to  mention  it  here.  It  was  not  the  inten- 
tion, in  expressing  the  above  view,  to  oppose  the  customary  method  of  designating 
this  harmony. 

Exercises. 


SiS^ 


-^ 


6$    % 


i 


£zz2z:^ 


t=| 


4. 

3 

2 

3- 

t 

=3- 

6 

4 

4 
3 

1 

v-^-\ 

H 

"^  rv 

-4— 

-A — 1 

-sJ~ 

-^ 

1— j 

a H 

g§^ 


ES 


J 

63       6 


-^r. 


4P40      6 
2   — 


MANUAL  OF  HARMONY. 


§i£ 


4 
6f        2 


6  60    6     3   3      6 


86S 


S 


Jl 


6    6$ 


S-a=I^E£ 


^^ 


^-gE 


!. 


1 — ^ 


I 


9.  3         6$ 


$  7^ 

4  6  5$ 

3  j- 


-^ — fg- 


7a 


1=5^ 


6     0  4  6   7 

7    4     5  3       J   4   53 


=^1^: 


1=F 


;h 


SStea 


6 


5  5lt    7 


-IK 


gi; 


7b 


6  $ 

6        4  - 
4        3  - 


^^ 


^ 


Note. —  It  is  much  simpler  to  explain  the  chord  of  the  augmented  sixth  and 
fifth,  when  it  occurs  in  minor,  as  a  seventh  chord  on  the  fourth  degree  (subdominant) 
of  the  scale,  with  an  altered  (raised)  fundamentat.  This  obviates  the  inconvenience 
of  being  obliged  to  recognize  "so-called"  chords  in  /rac/iV,?  while  ignoring  them  in 
theory.     It  is  easier  for    the  pupil  to  remember   that  the  chord  I  is  referred  to  the 

second  degree,  and  the  chord  5  to  the  fourth  degree,  than  to  be  obliged  to  study  out 

which  chord  it  is  that  has  been,  or  would  be  a  chord  of  the  ninth  had  it  not  met  with 
an  accident  in  losing  its  fundamental.  The  following  makes  this  much  discussed 
subject  clearer,  and  also  shows  that  the  subdominant,  as  usual,  presses  naturally 
towards  the  dominant. 

e  6 

5  4 

Original.  Altered.  Inverted.  Resolution  delayed. 


a^i^f 


a:  IV7 


-f 


m^ 


IV7 


See  Ex.  190,  at  c. 


112  MANUAL  OF  HARMONY. 

The  above  altered  chord  can  also  be  taken  as  standing  on  the  second  degree  of  the 
major  scale  ( as  above  in  C  ),  and  the  resolution  made  to  a  chord  of  the  sixth  on  the 
tonic,  thus : 

5  6 


i 


C:  117 


The  student  is  urged  to  become  perfectly  familiar  with  these  altered  chords,  as  they 
are  of  the  greatest  importance  in  the  art  of  modulating.  The  ease  with  which  they 
can  be  ioxm&di  from  dominant  seventh,  or  into  dominant  seventh  chords  makes  them 
very  valuable  aids  in  rapid  changes  of  key.  It  is  only  necessary  to  make  an  enhar- 
monic change  of  one  note;  thus  : 

0 

6  6 

1  ^ V*  4 


feg— i±^>^:^s= 


/f> ^o 51^ .xa I.I 


B\):  V7     a:  iVy  I  V?  I 

At  the  close  of  this  chapter,  we  review  oiice  more  the  broad  field 
which  it  has  opened  for  harmonic  formations.  We  have  found  much 
that  was  generally  known  and  useful,  and  much  appeared  which  was 
worthless  or  unfit  for  use.  Nothing  appeared,  however,  in  its  origi- 
nal state ;  everything  had  undergone  some  change,  an  addition,  or  to 
an  extent  an  embellishment.  This  forsaking  of  the  original  form 
gives  occasion  to  refer  again  to  what  was  said  on  page  104. 

While  it  was  a  long  time  before  these  harmonic  transformations 
were  discovered,  it  was  yet  longer  before  they  were  brought  to  prac- 
tical use.  Much  that  has  heretofore  seemed  unfit  for  use  may  yet, 
with  time,  be  perfected  ;  but  it  is  unadvisible  to  direct  the  whole  effort 
to  the  discovery  of  new  harmonic  formations  and  their  unwholesome 
use,  merely  from  a  desire  for  originality,  lest  we  lose  sight  of  the  more 
\n\Tporta.\\\.  J'tindame?2tal  principles  -which,  contain  the  healthy  germ  of 
art. 

All  these  transformations  should  serve  more  for  embellishment  in 
carrying  out  the  fundamental  idea,  and  unless  sparing  use  be  made  of 
them,  our  work  will  appear  overloaded  and  ourselves  be  regarded  as 
devoid  of  taste. 


MANUAL    OF  HARMONY. 


»i3 


At  the  close  of  the  presentation  of  all  the  essential  harmonies  and 
their  immediate  use,  we  append  a  table  giving  their  varieties 
and  derivations. 

View  of  all  the  Chords  belonging  to  a  Major  or  Minor  Key. 

I.     FUNDAMENTAL   HARMONIES. 
a.    The  triad. 


I 


b.    The  chord  of  the  seventh. 

1=11 


A.     The  Varieties   of   the    Triad:  Major,   Minor, 
Diminished,  Augmented. 

Major  Triads. 
Of  the  major  scale.  Of  the  minor  scale. 


C:T     IV       V  «:V     VI 

Minor  Triads. 


Of  the  major  scale. 


Of  the  minor  scale. 


m^     i^sa 


a:     I  IV 


C:    II        III       VI 

Diminished  Triads. 
Of  the  major  scale.  Of  the  minor  scale. 


C:  viio  a:     11°      viiO 

Augmented  Triad  of  the  Minor  Scale. 


J:. 

a:  III' 


N.  B.  For  other  augmented  triads  see  under  II.:     Altered  Chords. 
Inversions  of  the  Triads. 

a.    The  chord  of  the  sixth.  b.    The  chord  of  the  s^xth  and  fourth. 


114 


MANUAL  OF  HARMONY. 


B.     The  Varieties  of  the  Chord  of  the  Seventh. 

a.  The  chord  of  the  dominant  or  primary  seventh. 

b.  Secondary  chords  of  the  seventh. 

a.      Chord  of  the  dotninant  seventh  (  major  triad  with  minor 
seventh.) 

Formed  alike  in  major  and  minor. 
1  ^11 


C:  \\ 


i    0^^{m 


b.      Secondary  chords  of  the  seventh. 

1.     Major  triad  with  major  seventh. 

^     In  major. 


In  minor. 


2.     Minor  triad  with  minor  seventh. 

In  major. 


C:  11^     11I7     vi^ 
Diminished  triad  with  minor  seventh. 

In  major. 


^eJ 


^m 


C:  VIJO. 


Diminished    triad    with     diminished   seventh    (  chord   of    the 


diminished  seventh.) 


In  minor. 


a:  viio 


5.     Augmented  triad  with  major  seventh. 

In  minor. 


#^=0 


MANUAL    OF  HARMONY. 


IS 


Inversions  of  the  chords  of  the  seventh. 


a.     The  chord  of 
the  sixth  and  fifth 


b.    The  chord  of  the 
tth,  fourth  and  third. 


II.     ALTERED    (CHROMATICALLY   CHANGED)    CHORDS. 
The  augmented  triad,  formed  from  the  major  triad. 

In  major. 


b.     The  chord  of  the  augmented  sixth,  formed 

I.     From  the  minor  triad  with  raised  fundamental  (  so-called  double 
diminished  triad ) : 


i 


t=^%-=^^. 


2.     From  the  chord  of  the  seventh  of  the  second  degree  in  minor. 
(See  the  following  chords.) 

c.  The  chord  of  the  augmented  sixth,  fourth  and  third. 

d.  The  chord  of  the  augmented  sixth  and  fifth,  —  both  formed  from 
the  chord  of  the  seventh  of  the  second  degree  in  minor : 

Without  fundamental,     With  the  ninth  from 
Raising  of  Second  chord  of  the  fundamental 

the  third:  inversion.  aug.  sixth:  and  without  the  latter. 

:ig i=i^gg 


CHAPTER   XI. 


ON    MODULATION. 


The    term    modulation    formerly    signified    the   manner   in    which 
harmonies  were  arranged  to  a  given  part  or  melody.     By  it  is  now  un- 


jl6  MANUAL  OF  HARMONY. 

derstood  the  digression,  or  passing,  from  one  key  into  another.  The 
meaning  of  the  term  having  been  decided,  it  will  next  be  necessary 
to  learn  to  properly  recognize  and  define  each  occurring  modulation 
or  digression  into  a  foreign  key.  In  a  later  chapter,  the  means  by 
which  modulations  are  effected  will  be  more  fully  set  forth. 

A  modulation  takes  place  whenever  a  chord  appears  which  is  for- 
eign to  the  previous  key.  The  original  key  is  then  entirely  abandoned 
and  all  succeeding  chords  must  be  considered  as  belonging  to  the  new 
key  until  another  foreign  chord  is  introduced,  when  a  new  modulation 
will  naturally  arise. 


192. 


Thus,  in  the  above  example,  a  chord  appears  in  the  third  measure 
which  cannot  belong  to  the  key  of  C,  but  which  is  easily  recognized 
as  the  chord  of  the  diminished  seventh,  on  the  seventh  degree  of  d 
minor.  In  the  fourth  measure  we  find  the  triad  of  C,  which  now 
cannot  be  in  the  key  of  d  minor,  but  it  is  doubtful  whether  it  belongs 
to  C  major  or  to  G  major,  as  the  chord  may  belong  to  either  of  those 
keys.  [It  is  most  likely  that  in  this  case  it  belongs  to  G  major,  as 
this  modulation  is  decided  by  the  next  chord.]  The  concluding  mod- 
ulation to  a  minor  in  the  fifth  measure  is  evident  enough. 

The  chord  of  the  dominant  seventh^  and  also  the  chord  of  the 
diminished  seventh  are  the  most  decisive  means  for  modulating.  All 
other  chords  are  ambiguous,  as  they  may  belong  to  several  keys. 
Thus,  the  triad  of  G  major  does  not  belong  to  the  key  of  G  alone, 
but  is  also  the  dominant  of  C  major  and  c  minor,  the  subdominant 
of  D  major,  and  triad  on  the  sixth  degree  of  b  minor.  Owing  to  this 
ambiguity,  it  will  often  be  necessary  to  consider  the  situation  in  which 
a  chord  appears — that  is,  what  precedes  and  follows  it — before  decid- 
ing its  place  in  a  key.  A  decided  modulation  can  only  be  effected 
through  the  chord  of  the  dominant  seventh  or  its  inversions.  A 
musical  ear  will,  of  itself,  easily  grasp  a  modulation.      It  will  always 


MANUAL  OF  HARMONY. 


117 


take  the  foreign  harmony  as  being  the  one  which  is  nearest  related  to 
the  present  key.     Thus,  for  example,  in 


193.bfc=S:=u 


the  major  triad  of  D  taken  by  itself,  would  belong  to  the  key  of  D 
major,  but  in  connection  with  C  major,  the  ear  at  once  recognizes  it 
as  the  dominant  of  G  major,  and  the  following  chords  will  only  decide 
the  permanent  key.  The  following  exercises  are  for  practice  in  ascer- 
taining the  course  of  modulation.  The  markings  under  the  bass  should 
be  strictly  followed  in  all  cases  as  shown  in  the  first  exercise. 


Exercises. 


194. 


§tffi 


:fc# 


C:    I     C;V, 


I    C:  IV     V, 


:F=f 


S 


;==t 


w 


1e£ 


a 


§5 


6-7 

4-1 


^^m 


6$ 


ii8 


MANUAL   OF  HARMONY. 


7.        3         3 


4b      4         6b       6 
2        3  4         6 


6  6       6 

4         6       6 


^»$g#^F^^g#g^=&^&^ppS 


4  7  3  2  6 


gjr^^=i:tgs|g-^fE^'j=5=3fEjE;i^:=^ 


8  7b 


7      $ 

6       6       6 


4      ^  4b 

317    2       6  2 


r-r~£ 


i=^ 


ffi 


-<9      I  gy  g)- 


6       3 


2         7         47 


10.        8      6 


4 
3  3  6 


^^^s^^^^^m 


m 


^-^ 


if^ 


1$ 

6         Z% 


pi^i^^ 


0   ^    6 
6   3    4 


0 

^  4 

7    2        6       7     3 


^^^^ 


^-^js? ^- 


F=H— I — r 


en 


gy-pr^j — -.^^T — f^T=^ 


4=t: 


MANUAL    OF  HARMONY. 


19 


PART  II. 


ACCIDENTAL   CHORD-FORMATIONS.— TONES 
FOREIGN    TO    THE    HARMONY. 


CHAPTER  XII. 


SUSPENSIONS. 

The  simultaneous  progression  of  all  the  parts  of  a  chord,  especially 
when,  as  in  the  foregoing  examples,  there  is  no  variety  of  rhythm, 
occasions  a  certain  monotony  and  sameness.  Sometimes,  however, 
instead  of  all  the  parts  proceeding  at  the  same  time  from  one  chord 
to  the  next  following,  one  or  more  will  remain  stationary,  while  the 
remainder  proceed  to  their  respective  positions  in  the  succeeding  chord. 
The  most  important  of  this  class  of  progressions  is  termed  the  sus- 
pension. A  suspension  occurs  when  a  certain  expected  or  even  neces- 
sary progression  is  delayed  in  such  a  manner  that  a  voice  which 
should  descend  one  degree  in  order  to  take  up  its  position  in  the  suc- 
ceeding chord  remains  stationary,  while  the  other  parts  proceed  inde- 
pendently of  it.  The  delayed  or  suspended  voice  proceeds  to  occupy 
its  proper  position  later  in  the  measure.  Thus,  in  the  following  ex- 
ample— 


i 


9t 


H 


the  soprano  may  remain  on  C,  while  the  other  voices  take  the 
chord  of  G  in  the  second  measure ;  the  suspended  part  being  then  re- 
solved into  the  note  B  in  the  second  half  of  the  measure: 


1 


15^ 


I 


120 


MANUAL    OF  HARMONY. 


In  the  same  manner  a  supension  can  be  formed  from  Ex.   No.    195 
by  delaying  the  tenor  : 


1 


ifc 


ist 


The  principal  feature  of  the  supension,  is  that  it  generally  forms  a 
dissonance  with  the  chord  in  which  it  appears,  and  acts  as  a  means  for 
the  closer  connection  of  harmonies  through  the  expected  resolution  of 
the  dissonance.  That  the  dissonant  character  of  the  suspension  does 
not  always  exist  is  shown  in  Ex.  197,  where  the  suspension  is  not 
dissonant  with  any  interval  of  the  chord,  but  only  a  chord  of  the  sixth 
over  the  bass  note  G.  In  this  case  the  unusual  appearance  of  the 
minor  triad  on  the  third  degree,  between  the  triads  of  the  first  and 
fifth  degrees,  as  well  as  its  peculiar  position,  together  with  the  delayed 
progression  of  the  tenor,  all  combine  to  give  the  phrase  the  character 
of  the  suspension.  The  necessary  rules  for  forming  suspensions  are 
given  in  the  above  examples  : 

A  suspension  may  be  formed  by  delaying  the  progression  of  any 
voice  which  would  naturally  descend  one  degree,  provided  the  tone 
which  forms  the  suspension  be  prepared.  The  suspension  in  its  com- 
plete form  may  therefore  be  considered  under  three  heads,  namely, 
the  preparation^  the  suspension  itself  and  its  position,  and  its  res- 
olution^ or  progression. 

a.  The  preparation. 

The  preparation  of  a  suspension  is  precisely  like  that  of  any  other 
dissonance,  and  may  be  effected  by  means  of  any  one  of  the  intervals 
of  a  triad,  and  also,  though  more  rarely,  by  means  of  a  seventh,  gen- 
erally the  dominant  seventh. 


Preparation  through  the 
octave  of  the  fundamental: 


-^— tgp- 


1^2 


Through  the  third: 


aiSii 


C:I 


I     a:  VII07 


C\  I 


MANUAL   OF  JIAkMONY. 


$ 


Through  the  fifth 


m 


^ 


I  ^ 


C:  I     G:  V 


VI     C:  I 


IV 


I    e:  viio. 


Through  the  dominant  seventh. 


I 


^- 


C:  Vt 


V7 


a:  V 


The  preparation  must  take  place  on  the  unaccented  part  of  the 
measure  (arsis)  ;  the  suspension  enters  on  the  accented  part  (thesis). 
The  note  of  preparation  must  be  a^  least  as  long  as  the  suspension 
itself,  in  conformity  with  the  rule  previously  given  for  the  preparation 
of  dissonances. 

b.  The  suspension. 

The  entrance  of  the  suspension  on  the  thesis  has  been  mentioned, 
but  its  position  in  other  respects   must  be  more  minutely  explained. 

The  suspension  may  appear  in  any  voice  and  before  any  interval  of 
the  triad, ^ — before  the  seventh  very  seldom. 


I 

199.  / 


Suspensions  before  the  octave  of  the  fundamental. 


C:  V7       I 


|=g^5fe 


m 


V7     I 


V7 


m 


MANUAL  OF  HARMONY. 


Before  the  third. 


J=E=«=d= 


5       _ 
4       3 


,^i 


ii 


^ 


Before  the  fifth  seldom,  only  in  certain  positions. 
a.  _       b.  c. 


C:\ 


V7       C:  I 


The  remarks  on  Ex.  197,  will  apply  to  all  suspensions  before  the 
fifth.  Thus,  in  the  above  example  the  progressions  at  a  and  c  will 
have  the  entire  character  and  effect  of  suspensions,  while  that  at  a^  will 
not.  If  a  seventh  be  added  to  the  chord  into  which  the  suspension  is 
resolved,  as  at  b  in  the  above  example,  the  dissonance  of  the  suspen- 
sion is  at  once  perceived;  also  at  e.  The  reason  why  the  seventh  can 
seldom  be  suspended,  is  that  the  suspension  would  in  most  cases  form 
a  perfect  octave,  and  as  such  would  not  have  that  dissonant  character 
which  is  essential  to  a  suspension.  If,  however,  the  octave  be  dimin- 
ished instead  of  perfect,  a  suspension  of  the  seventh  is  "possible,  as  at 
b  in  the  following  example : 


^-^ 


w 


The  progression  at    a  in  the  above  example  is  called   a  passing 
seventh. 


MANUAL  OF  HARMONY. 


»3 


c.     The  resolution. 

The  resolution  of  the  suspension,  as  before  remarked,  takes  place 
by  the  same  voice  descending  one  degree. 

Remark. — different  ways  of  making  resolutions  will  be  treated  later. 

It  should  here  be  observed,  that  the  tone  of  resolution  (the  tone 
which  has  been  delayed)  must  not  appear  in  any  other  voice  except 
the  bass. 


P 


b.  Better. 


J=i 


.-=U L 


\^     e^- 


WE^ 


-<2U^,2_ 


±^ 


-%- 


^^Ei^T^- 


In  example  a,  the  tenor  moves  from  A  to  C,  the  C  being  also  the 
resolution  note  of  the  soprano ;  in  example  c,  the  tenor  takes  the  note 
G  which  is  already  suspended  in  the  alto.  Both  of  these  cases  are 
faulty,  especially  because  the  third  and  Jiftk  of  the  chord  are  doubled. 
The  effect  of  doubling  the  ftinda?7iental^  as  in  example  d^  at  N.  B., 
is  better,  particularly  when  the  natural  flow  of  the  voices  require  it, 
as  in  the  following  passage  : 


Fundamental. 


Third. 


Remark. — It  may  be  here  observed,  that  when  the  fundamental  is  doubled  it  should 
always  be  at  a  distance  of  at  least  an  octave  from  the  suspended  note,  and  that  doub- 
ling in  the  unison  is  to  be  avoided,  e.  g. 

^ \ 


m 


^ 


Between  bass  and  tenor,  however,  such  a  progression  as  the  above  may  be  possible. 


124 


MANUAL    OF  HARMONY. 


Other  intervals  besides  the  fundamental  may,  however,  be  doubled 
in  the  bass.  That  voice  being  the  one  which  determines  the  chord, 
has  the  power  of  resisting  the  dissonance  of  the  suspension,  and  such 
doublings  are  therefore  admissible  if  the  intei^val  so  doubled  be  intro- 
duced by  a  good  leading  of  the  voices,  e.  g. 


2.0)3. 


Faulty. 


The  fault  contained  in  the  last  example  becomes  j^lain  if  the  sus- 
pension be  omitted,  when  open  octaves  will  be  found  between  soprano 
and  bass : 


te 


e 


It  is  the  same  with  fifth   progressions  which  are  covered  by  the 
suspension : 


J— I- 


Wmm 


These  remarks  may  be  condensed  into  the  following  rule : 
The    suspetision    does    not    remove  parallel  octaves   and  Jifths. 
Hence,  the  following  is  faulty. 


MANUAL    OF  HARMONY.  125 

Nevertheless,  paralled  Jift}is^  covered  by  suspensions,  are  not  to  be 
unconditionally  forbidden.  Their  employment  is  rare,  however,  and 
must  depend  on  the  leading  of  the  other  parts  being  such  that  the  un- 
pleasant effect  of  open  fifths  is  not  perceived.  It  is  impossible  to 
give  positive  directions  regarding  them,  and  to  reject  them  totally 
would  be  going  too  fai. 

The  suspension  in  the  bass^  which  usually  occurs  before  the  third 
of  the  chord,  or,  which  is  the  same  thing,  before  the  chord  of  the 
sixth,  or  the  sixth  and  fifth,  does  not  allow  the  suspended  ttote  to  ap- 
pear in  any  other  part. 


The  suspensions  before  the  fundamental,  and  the  fifth,  are  seldom 
used  in  the  bass.      See  Ex.  199,  at  the  end. 


208. 


The  method  of  figuring  the  suspension  has  already  been  partly 
shown  in  the  foregoing  examples.  When  the  suspension  lies  in  one 
of  the  three  upper  parts,  the  interval  found  between  the  suspension 
and  the  bass  is  indicated,  together  with  its  resolution. 

For  example  :|-,  9  8,  7  6.  Where  necessary,  other  figures  are  added 
to  indicate  the  chord  into  which  the  suspension  is  resolved,  c.  ^.,  the 
chord  of  the  sixth  H,  the  chord  of  the  sixth  and  fourth  6-  or  4^. 

If  the  suspension  lies  in  the  bass,  or  lower  voice,  the  accidental 
intervals  of  the  upper  voices  are  indicated  by  figures,  e.  g.,  |-,  or  if 
it  be  a  chord  of  the  seventh  4-,  the  dashes  signifying  that  the  voices 
remain  stationarv  during  the  resolution  of  the  suspension. 


126 


MANUAL    OF  HARMONY. 


The  suspension  in  the  bass  is  also  indicated  by  an  oblique  line  ovei* 
the  suspended  note,  and  the  proper  figuring  over  the  note  of  resolu- 
tion ;  for  example : 


i 


^ 


I 


^ 


T=^ 


-gr-Y^- 


In  the  following  exercises  the  former  manner  is  adopted,  as  the 
most  usual.  . 

Note. —  As  the  suspension  is  not  considered  a  real  harmony,  it  will  be  necessary 
when  adding  the  Roman  numerals  under  the  bass,  to  make  them  apply  to  the  fun- 
damental of  the  resolution,  which  is  the  real  chord.  An  examination  of  No.  211  will 
show  how  these  exercises  are  to  be  worked  out.  It  should  also  be  observed,  when 
the  figure  7  is  followed  by  a  6  over  the  same  bass  note,  that  it  does  not  imply  a 
chord  of  the  seventh,  but  a  chord  of  the  sixth  with  the  sixth  suspended  by  the  seventh. 
See  No.  211,  third  measure. — Ed. 

Exercises. 


o.  I 


5  - 
4  3 


7   6 
5  _ 


5  7 
4  3 


g5^='^^^giiigiga]lgg-^^gf^ 


IV       V7 


117   V7    I 


6  7 

41t 


:b 


^i 


4=tFi=3:^ 


3.  3 


s3e 


5  - 
2 


6      3G 


98      2 


62 


si^E^^ 


S3 


^ 


6 

't4  ° 


75*— "g- 


^a 


MANUAL  OF  HARMONY. 


127 


7  6tJ 

4  7       7 

98         3  -       6  6b    J 


a^ 


6  5-6 

6  4  3      6 


ilH 


-^ 


^^m 


7  $ 

4         6 
6      3-4        2         7 


-t9-h^ 


:[=£[= 


:if^ 


4:^^ 


6  5- 
6        4  4  3$ 


Ft 


Ei$S: 


68 

5-  5        -  ^  3 

8         6         432         620^  3b6       2 

^ r-^r ^-~-:=jn .:  d. 


4=^: 


s*— V 


ay|^=j^;^gEg 


987        5 


6 
6         4 


6 

5     3     7 


7  6 

4- 
76  -      3  2         6 

6-      6 
4  3       4 

765 

-?d ^ 

7 

—  : H 

-^^-^ 1 

Lrt      ^ 

="-^ 

3^.J 

In  working  out  the  above  exercises  it  will  be  advisable  to  write 
each  voice  on  a  separate  line  or  staff,  both  in  order  to  obtain  a  cleai'er 
view  of  the  progression  of  each  part,  and  also  as  a  useful  preparatory 
exercise  in  reading  from  score.  Inasmuch  as  the  four  different  parts 
are  always  considered  as  vocal  parts,  it  will  also  be  better  to  write 
each  part  in  the  clef  which  properly  belongs  to  it,  instead  of  the 
violin  clef  as  heretofore.  Familiarity  with  these  clefs  is  necessary  in 
the  study  of  counterpoint,  and  they  are  easily  learned  by  practice  and 
comparison  with  those  already  known. 


Remark.  —  A  knowledge  of  the  alto  and  tenor  clefs  is  indispensable  for  the  read- 
ing and  understanding  of  scores,  as  many  voices  and  instruments  have  their  parts 
written  entirely  or  partially  in  then), 


128 


MANUAL  OF  HARMONY. 


The  clef  proper  to  be  used  by  the  soprano,  alto  and  tenor,  is  called 
the  C  clef.  For  the  lowest  voice,  the  bass,  the  F,  or  bass  clef 
is  still  used. 

The  position  of  the  C  clef  always  indicates  the  once  marked  (mid- 
dle) C,  and  for  the  soprano  this  C  is  placed  on  the  Jirst^  for  the  alta 
on  the  thirds  and  for  the  tenor  on  i\\e  foztrth  li'nc^  e.  g. 


Soprano  clefs. 


h^' 


3SEES 


=a 


Tenor  clefs. 


The  ordinary  compass  of  the  voices  in  these  clefs,  as  well  as  the 
relative  position  of  the  same  notes,  is  clearly  shown  in  the  following 
example :  ^ 


i 


fm 


^- 


:i=^ 


-t-^- 


V^ 


v^ 


I  I 


Soprano  clef. 


^^ 


T=p= 


^^^ 


Alto  clef. 


i^ 


, Li   * 


Tenor  clef. 


^— • 


fc^.^^^^ 


m 


9i=J: 


^ 


\m^ii 


t^^^ 


Probably  the  best  method  of  fixing  these  clefs  in  the  memory,  is  to 
carefully  observe  the  position  of  the  C  triad,  written  for  the  different 
voices;  then  the  neighboring  tones  are  easily  found.  Thus  the  posi- 
tion of  the  C  triad,  with  the  fundamental  doubled,  will  be : 


In  the  soprano : 


t3=«---- 


MANUAL    OF  HARMONY. 


29 


In  the  alto 


-«-  c 


In  the  tenor,   best    in  the   position  of    the 
chord  of  the  sixth  and  foin'th  : 


-#-0 


The  first  exercise  of  No.  210  worked  out  in  these  clefs  follows  here 
21  1. 


TtT-^^— -f^ ^- 

— — L 1 

^  1  rj — ^- 

^1 

F=5=i; 

Itaiji f= — 

—  -i9 (^ f5>—  -G>~ 

£i£d=d 

— =1 

5    - 
4   3 

Rf  Ttr ~ 

1 <s~ 

!    1    1 

=  J 

5'"0^ 



:"_s 

C:      I  V 


F  Gf     C      dn 

IV  V7     I      117 


V7 


The  working  out  of  these  exercises  will  require  a  somewhat  free 
treatment  of  the  voices  with  respect  to  their  leading,  since  in  order  to 
obtain  a  good  position  for  the  suspensions  it  will  often  be  necessary 
to  lead  the  voices  by  skips,  thereby  bringing  the  chord  into  opc?i  posi- 
tion, which  may  again  be  exchanged  for  close  position,  through  the 
natural  progression  of  the  voices.  In  thus  altering  the  position  of  the 
voices,  the  following  rules  must  be  observed  : 

It  is  not  permissible  for  all  the  voices  to  change  their  proper  posi- 
tions at  once,,  when  passing  from  one  chord  to  another.,  or  in  passing 
from  close  to  open  position,  or  vice  versa.,  except  in  certain  cases 
where  one  and  the  same  chord  is  changed  to  another  position.  Any 
voice  may  change  its  position,  if  one  or  more  voices  rc7nain  stationary. 

The  eighth  exercise  of  No.  210,  worked  out  as  follows,  will  show  the 
application  of  the  above  rule : 


130 

212. 

SOFRANO. 


MANUAL  OF  HARMONY. 
2  3 


5     N.B. 


S5S= 


-15'- 


-^-fS*- 


:t=:t 


(2^9- 


^eE 


P5^S^ 


^t=f: 


9     8       7 


4i=tt 


-^— (S*- 


;^^3 


g      -      c        -     7     ^707    ^       /r7    B\)    E\>    B\,     CI    F 
g:  \       -       IV      -     7    Ii07>5b:lll  V7      I     IV     I    F:\1    I 


^--. 


:p=t: 


7   7 

^b;VT 


fflS^ 


:l=-^ 


=^4 


-(S-^"- 


s 


7    6 
5    - 


4    -  5-6 

32643        4        76       5 


5     I      7 


9i^ 


i=± 


:}i!2 — ^. 


s'-'g- 


I 


Dt    g       c 
V7    I         IV 


/^7        ^b^ 
^b:V7       I     II 


^"■-    I 


iS'b  "°7   >9    7 
VI  li«^7    V    7 


The  following  will  explain  this  treatment: 

The  close  position  in  which  the  above  example  begins  is  exchanged 
in  the  fifth  measure  for  open  position,  which  continues  until  the  elev- 
enth measure,  when  close  position  appears  again. 

This  variety  of  position  was  due  to  a  freer  leading  of  the  soprano 
and  tenor.  In  the  fifth  measure,  the  soprano  skips  from  its  natural 
position  to  the  seventh.,  El2  (at  N.  B.),  a  skip  which  is  good  when 
the  J'ti?idat}tental  is  already  present  in  the  previous  chord,  as  here  the 
F  in  the  bass.     Again,  in  the  seventh  measure,  the  soprano  leaves  its 


MAlsrUAL  OF  HARMONY. 


'31 


position  and  skips  to  the  fifth  of  the  chord,  the  other  farts  remaining 
stationary,  whereby  the  suspension  appears  in  a  better  position.  Fi- 
nally, the  close  position  is  resumed  at  the  end  of  the  tenth  measure  by 
means  of  a  free  movement  of  the  tenor. 

Suspensions  from  Below;   Resolving  Upward. 

Suspensions  from  below  are  only  regarded  as  such  in  a  few  individual 
cases.  Most  progressions  of  this  kind  are  caused  by  a  shortening  or 
contraction  of  an  ordinary  suspension  followed  by  an  upward  move- 
ment, e.  g. 


■ST       -G> 


The  suspension  from  below  may  be  formed  by  delaying  the  pro- 
gression of  the  leading  tone  : 


and  also  with  many  intervals  which  ascend  a  half-step,  especially  in 
the  case  of  those  chromatically  altered  chords  which  contain  aug- 
mented intervals,  e.g. 


215. 


Observe,  that  as  in  the  case  of  suspensions  from  above,  the  note  of 
resolution  must  not  be  found  in  any  other  voice  except  the  bass. 
The  last  of  the  above  examples  gives  us  the  combination  which  has 
already  been  found  as  a  chord  of  the  seventh  on  the  first  degree  of  the 
minor  scale,  and  which  was  pronounced  unfit  for  use  as  a  fundamen- 


J 2 2  MANUAL  OF  HA RMONY. 

tal  harmony.  It  is  evident,  however,  that  when  employed  as  above, 
it  is  only  to  be  explained  as  a  suspension  (or  retardation)  of  the  lead- 
ing tone. 

Of    other  suspensions,   especially    those  progressing  a  ivhole-step 
upward  : 


216. 


J__l'___^-.f«-J_i''-^4^>^4-J 


J- 


ii^Elife-liii^jsi] 


some  show  in  themselves  their  unnatural  progression  ;  while  others, 
however  often  they  may  find  place  in  practice,  in  theory  must  be 
condemned  as  unfit  for  use  in  pure  part-writing.  Should  these  irreg- 
ular suspensions  be  carried  out  in  the  manner  shown  in  No.  213,  the 
faulty  progressions  upon  which  they  are  based  would  show  them- 
selves : 

.      d.      , 

1-^-    -       \^_ 


a.  b.  ^  c.  1,1       ^  1*1      l^- 


Suspensions  in  Two  or  More  Voices. 
Suspensions  may  appear  in  two  or  more  voices  at  the  same  time : 


Suspensions 

in  two  voices.  Ii>  three  voices. 


.    I  1^     I  I 


\^%% 


The  chord  of  the  sixth  and  fourth  often  appears  as  a  douole  sus- 
pension, e.  g. 


-<s- 

Freer  Movement  of  the  Voices  in  Resolving  Suspensions. 

Hitherto,  only  two  chords  have  been  employed  for  tlie  preparation, 
entrance,  and  resolution  of  the  suspension,  since  the  voices  not  par- 


MANUAL   OF  HARMONY. 


133 


ticipating  in  it  remained  stationary  during  the  resolution.  The  pro- 
gression of  the  voices  will,  however,  become  richer  and  more  varied 
if  three  chords  are  introduced. 

This  is  effected  by  allowing  one  of  the  voices,  generally  the  bass, 
or  even  several  at  the  same  time,  to  proceed  to  a  new  harmony  at  the 
same  moment  that  the  suspension  is  resolved.  The  note  into  which 
the  suspension  resolves  will  always  form  one  of  the  intervals  of  such 
new  harmony. 

For  example : 

By  progression  of  the  bass  : 

-,-4— J I V-. ._^^i_J_J V 


.^^ztg: 


-z^-^g^ 


^ 


-(=2- 


ii 


W^^. 


=8f 


C:  V7        I 


IV      117       I    a-.vn^i 


By  progression  of  several  voices ; 


ll^g^S 


t^ii-=t 


^f 


1 


1 


V=^ 


C:  I 


V7 


IV    viio     VI 


I         V7  a:  V7     I 


In  all  these  examples  the  resolution  of  the  suspension  follows  reg- 
ularly while  the  other  voices  progress  to  a  new  harmony  of  which 
the  resolution  tone  forms  a  part. 

Remark. — In  illustration  of  the  views  advanced  in  Chapter  IX,  on  the  subject  of 
chords  of  the  ninth,  it  may  here  be  observed,  that  many  cases  in  which  the  ninth 
occurs,  and  which  would  be  recognized  and  treated  by  many  theorists  as  chords  0/ the 
ninth,  may  be  much  more  simply  explained  by  considering  them  as  suspensions  of  a 
ninth  zvith  the  use  0/ three  chords,  thus : 


Suspension  of  a  ninth 
with  two  chords.        With  three  chords.      Better, 


J- 


iii^^f=i 


'34 


MANUAL    OF  HARMONY. 


Of  the  ninth  which  enters  free,  more  will  be  said  when  treating 
organ-point. 

It  may  still  be  urged  as  an  argument  against  independent  chords  of 
the  ninth,  the  impossibility  of  bringing  them  into  such  inversion  -with 
the  fundamental  that  the  latter  is  brought  into  close  proximity  with 
the  ninth,  as  may  always  be  done  in  the  case  of  chords  of  the  seventh, 


$ 


I 


-r — r — — 

In  like  manner  fozir  chords  may  be  employed  for  the  preparation 
and  resolution  of  a  suspension,  provided  the  tone  of  resolution  is  not 
contained  in  any  other  voice,  e.  g. 

Without  suspension. 


C:  I  IV      II    vijO       V 


Exercises. 


3-  5        6  5 

1.    8  7   9        6        4 ^  7_    4        7  6 6 


n 


2.       82    2        6 


S=ii^^^ 


67665  4  «S„ 

4        5-5       4        6-^3  6747 


^^EEEEEF 


^=^ 


6  9         7        47 


1^^^^^^^ 


MANUAL    OF  HARMONY. 


'35 


7^4         2 


^ 


6  75      9 


6 

4  6 


gg^^ 


6  6        $ 

4        6        6 


6 

4        6 


p^trTf'-=g^^P5gg^^^^&g=J:-J^ 


6 

«  7 


6         6 

5         4         7 


7 

46  6        6 

8  2  4  4  6 


^fcE 


:S=1 


liSi^gE^I 


7 
7  4 


§^F=F 


7         36 


k 


5 

4        6 


^Em 


2        7  4    7 


6         6 
5         4  7 


=9isfe.^ 


EE 


5 
6        4 


IS 


EP^H 


^ 


:?=•" 


S3 


5 
4  3 


ft?=e^ 


="=sg^Fs^ 


H^pE 


7  6  7- 
4-6  5 

%  32      6 


s^ 


£? 


9       6        4 


l^i^pl^llH 


Between  the  suspension  and  its  resolution,  other  tones  may  be  in 
serted  in  the  same  voice. 

These  may  be  tones  which  belong  to  the  chord,  e.  g. 


^=ptd=^ 


^-Stg: 


i^st 


^ 


:^- 


27^        <& 


or  tones  foreign  to  the  harmony,  changing  notes,  c.  g. 


*: 


.il 


^C#'    LJCJ- 


^' 


g 


:s=±^ 


,-5  MANUAL    OF  HARMONY. 

The  explanation  of  these  and  similar  cases  will  be  more  complete 
when  describing  passing  and  changing  notes.  Cases  are  to  be  met 
with  in  which  the  suspension  has  no  resolution  whatever,  e.  g. 

Usually  thus: 

^__^_^ -^-     ^-*-'        N 

228.  "^  '' 


Such  passages  are  formed  by  the  omission  of  one  or  more  notes  of 
the  following,  or  some  similar,  phrase  : 


229. 


Anticipation. 

The  anticipation  of  a  tone,  which  is  the  opposite  of  a  suspension, 
and  is  less  frequently  used,  occurs  when  one  or  more  voices  proceed  to 
their  places  in  the  following  chord  before  the  others,  or  before  the 
rhythm  would  lead  us  to  expect  them,  thus  giving  rise  to  temporary 
discords. 

Progressions  of  this  sort  seldom  occur  in  slow  movements  or  with 
long  notes,  on  account  of  the  harsh  effect  of  the  dissonances  which 
they  occasion.  It  is  only  the  shorter  divisions  of  the  measure  that  are 
anticipated,  e.  g. 


Anticipation  in  the  bass. 

-X 


In  the  soprano. 


In  several  voices. 


^^^ir-^-t 


mw^rn^ 


MANUAL    OF  HARMONY. 


37 


The  similarity  of  the  above  to  what  is  known  as  syncopation  is  un- 
mistakable, but  the  latter  is  formed  not  by  anticipating  \.\\<i.  chords,  but 
by  striking  after. 

The  movement  of  the  voices  may,  under  some  circumstances,  be 
more  free.  The  note  which  forms  tlie  anticipation  need  not  always 
be  exactly  the  one  which  is  expected  on  the  appearance  of  the  second 
chord.  A  different  note,  if  it  belongs  to  the  harmony  of  the  second 
cliord,  may  also  be  introduced  as  an  anticipation,  as  in  the  familiar 
cadence : 

*  Or.  * 


I  I 


Another  kind  of  rhythmic  variety,  the  reverse  of  anticipation,  occurs 
when  one  voice  does  not  proceed  to  its  place  in  a  chord  until  after  all 
the  other  voices  have  taken  up  their  respective  positions.  Such  pro- 
gressions resemble  suspensions,  inasmuch  as  both  preparation  and  res- 
olution take  place,  but  differ  from  them  in  the  important  particular, 
that  thev  are  formed  by  rhythmic  rather  than  harmonic  variations, 
and  can  only  appear  in  sequences,  whereas  suspensions,  whether 
singly  or  in  greater  numbers,  appear  under  entirely  different  condi- 
tions. 

The  following  bass  presents  a  series  of  such  after-struck  tones : 


Allegro. 


2.32.. 


1 


r^t — r 


=F^^ 


M- 


I 


pfc 


I 


iSE 


'^- 


iii- 


^ 


'38 


MANUAL    OF  HARMONY. 


The  unison  passage   in  Beethoven's  "  Leonore  "  overture    (No.  3) 
would  be  classed  under  this  head : 


I 


hA 


^-"K 


psi 


4=:i; 


3^93 


1}=^ — j— L=t 


—I — flH i — t-H 1 


J_.4— J- 


r^  -=^: 


¥ 


v=^ 


'^^^^^^^^^^^^ 


i 


-m- 


fe 


i^l 


1^ 


s=t 


^ 


5^-=^l — ^ 


^^ 


ii=p=:|t 


-^-    -^- 


■^=^ 


V^ 


m 


CHAPTER    XIII. 


ORGAN-POINT  :    SUSTAINED    TONES. 


By  sustaining  one  or  more  voices,  and  by  the  chords  thus  accident- 
ally formed,  a  peculiar  variety  of  harmonies  are  produced.  We  fre- 
quently find,  usually  in  the  bass,  a  long  sustained  tone  over  which  the 
other  voices  progress,  apparently  without  any  reference  to  it.  When 
this  tone  lies  in  the  bass,  it  is  called  organ-point,  or  pedal-point. 
When  occurring  in  the  other  voices,  they  are  called  sustained  tones,  or 
stationary  voices.  The  tones  adapted  for  these  sustained  voices  are 
the  ionic  and  dominant ;   they  are  also  used  together. 


MANUAL  OF  HARMONY. 


'39 


Remark.  —  Attempts  which  have  been  made,  by  many  composers,  with  the  third 
of  the  triad,  sound  unnatural  and  far  fetched. 

The  harmonic  connection  and  progression  of  the  remaining  voices 
during  the  continuance  of  the  organ-point,  is  still  carried  out  accord- 
ing to  the  rules  already  known,  the  lowest  of  them  being  treated  as 
the  harmonic  foundation,  and  usually  without  regard  to  the  sustained 
tone. 

Before  entering  into  details  regarding  the  treatment  of  the  organ- 
point  some  examples  may  follow  : 

a.    Organ-point  upon  the  tonic. 

"         I         I     J.        '  " 


b.      Upon  the  dominant. 


e 


J-* 


r-\ 


^-- 


1.^^ 


I  I 


r-|  r  r  j  r  *  I  -^ 


§ie 


fP^f^^^^Sf 


:3^ 


il 


iTTT" 


is: 


^ 


Upon  both  together. 


iiB: 


iCis: 


t^Si 


T^ 


Its: 


140 


MANUAL    OF  HARMONY. 


In  the  above  examples  the  chords  to  which  the  organ-point  does  not 
belong  harmonically  are  marked  with  a  cross. 

The  following  remarks  may  serve  for  the  treatment  of  the  organ- 
point  : 

1.  The  entrance  of  the  organ-point  must  be  at  a  rhytJunically 
definite  time; 

2.  By  means  of  a  chord  to  which  the  organ-point  harmonically 
belongs ; 

3.  The  last  chord  of  the  organ-point  must  also  harmonize  zvitk 
it. 

The  first  takes  place  at  the  beginning  or  end  of  a  period,  or  a  sec- 
tion of  one,  and  upon  the  accent ;  the  second  and  third  generally 
through  the  fundamental  of  a  triad,  as  in  Ex.  234  a,  c,  d.,  or,  as  at  (5, 
through  the  chord  of  the  sixth  and  fourth. 

It  must  be  borne  in  mind,  that  chords  foreign  to  the  bass  tone 
should  not  follow  each  other  too  frequently,  but  alternate  with  those 
which  belong  harmonically  to  the  organ-point.  This  is  necessary  in 
order  to  avoid  digressions  conti"ary  to  the  character  of  the  organ-point, 
which  is  to  hold  firmly  together  the  various  chord-connections. 

Thus,  the  following  organ-point  would  be  faulty  in  this  respect : 


The  voice  lying  next  above  the  bass,  in  a  four-part  phrase,  the  tenor, 
becomes,  in  case  of  the  organ-point,  the  basis  for  the  harmonic  lead- 
ing. Hence,  all  the  necessary  harmonic  progressions  must  rest  upon 
this  voice,  even  though  the  organ-point  should  accidentally  belong  to  the 
harmony.  Thus,  in  Ex.  234,  a,  the  progression  of  the  B1?  in  the  alto 
(in  the  first  measure)  is  determined  by  the  leading  of  the  other  voices, 
and  not  because  it  is  the  seventh  from  the  bass. 

When  the  organ-point  rests  upon  the  dominant,  as  often  happens 


MANUAL  OF  HARMONY. 


141 


at  the  close,  no  plagal  close  can  be  formed  over  it,  as  appears  from 
the  third  rule  cited  above,  e.  g. 


^s^4mmmm 


The  plagal  close  may,  however,  be  used  with  the  organ-point  on 
the  tonic  : 


237.< 


The  end  of  the  organ-point  must  be  treated  just  as  carefully  as  its 
entrance.  In  the  above  examples  this  takes  place  through  a  cadence, 
where  it  presents  no  difficulty,  except  in  cases  like  No.  236.  The 
organ-point  may,  however,  pass  earlier  into  the  harmonic  movement, 
when  the  third  rule  must  be  strictly  observed,  e.  g: 


^ 


238. 


^ 


t=4: 


r\ 


^— •- 


Sfc 


3^ 


I  I 


• — • — s — <& 

f— >    t    i--^ 

'    1    I    r  I 


I 


i_^eEE 


Its: 


t^ 


•-#- 


^ 


I 


To  break  off  in  the  following  manner  would  not  be  good 


I        I  etc. 


§iE: 


^^ 


£P 


142 


MANUAL  OF  HARMONY. 

Stationary  Voices :  Sustained  Tones. 


Sustained  or  stationary  voices  in  the  upper  parts  are  less  frequent 
than  the  organ-point,  and  require  more  careful  treatment.  Sustained 
tones  of  this  sort  only  suit  the  character  of  these  voices  when  the  chords 
not  belonging  to  them  appear  but  seldom,  as  these  voices  have  not 
the  power  to  counterbalance  the  effect  of  the  foreign  chords,  which  is 
a  pecuHarity  of  the  bass  as  the  voice  which  determines  the  harmony. 

Thus,  the  organ-point  in  Ex.  234,  a,  if  placed  above  the  other  voices, 
will  not  sound  well  in  the  last  measures : 


240. 


but  the  following  with  the  dominant  as  the  sustained  tone,  is  better, 
because  the  last  chords  belong  to  it : 


The  "  Gloria"  of  Cherubini's  Mass  in  C-major,  contains  an  exam- 
ple of  the  effective  treatment  of  the  sustained  tones,  where  an  Ab  in 
the  violins  is  held  for  some  time  while  the  chorus  and  the  other  instru- 
ments carry  out  their  respective  parts  below;  also  the  D  of  the  violins 
in  the  introduction  of  Mendelssohn's  overture  "Calm  Sea  and  Happy 
Voyage."  In  either  example  few  chords  are  found  which  do  not  con- 
tain the  sustained  tone  as  one  of  the  intervals.  The  Trio  of  the 
Scherzo  of  Beethoven's  Symphony  in  A,  contains  an  A  which  appears 
as  stationary  tone  in  the  upper  and  middle  voices,  and  also  as  organ- 
point  below,  and  which  serves  as  harmonic  basis  throughout  the 
movement. 

Stationary  tones  in  the  middle  voices  require  as  careful  management 
as  those   in  the   upper  voice.     In   instrumental  works  they  may   be 


MANUAL    OF  HARMONY. 


143 


doubled  according  to  circumstances ;    they  rarely  occur  in  four-part 
writing,  and  not  at  too  great  a  length,  e.  g. 


m 


i  J. 


t^-r 


I    r  I 


I 


9i=E 


rt^yr 


Remark. — In  addition  to  what  has  been  said  of  the  chords  of  the  ninth,  the  follow- 
ing may  still  find  place  : 

In  the  above  Ex.  b,  if  the  stationary  tone  be  included,  a  complete  chord  of  the  ninth 
is  found,  inverted,  and  with  a  regular  resolution.  The  objection  to  chords  of  the 
ninth,  as  already  stated,  is,  that  they  cannot  be  inverted  so  that  the  fundamental  and 
ninth  can  be  brought  into  close  proximity,  as  is  the  case  with  sevenths.  That  they 
may  occur  together  at  a  greater  distance,  as  above,  is  no  reason  for  regarding  them 
as  independent  chords,  as  they  only  occur  in  connection  with  a  stationary  tone,  the 
character  of  which  is  to  carry  harmonies  foreign  to  it,  as  for  instance,  in  the  case  of 
the  following  ninth,  which  surely  forms  no  chord  of  the  ninth. 


243. 


=^=5= 


^^^^^- 


^\ 


^^ 


mm 


m^ 


f=t 


^^ 


I 


When  the  harmonic  progression  above  the  organ-point  is  to  be  indi- 
cated by  figures,  the  intervals  above  the  stationary  tone  must  be  given, 
thus  changing  sometimes  the  usual  figuring  of  the  chords.  The 
organ-point  in  No.  234,  6,  might  be  marked  thus  : 


6  —  76 
4  —  5    3fc 


7    6 
4    4 


244. 


gt 


7    6    7  7 
6    4         4 


8 
6    4 
7  4    2    7 


i 


On  account  of  the  difficulty  of  reading,  as  well  as  its  lack  of  com- 
pleteness, this  method  of  marking  is  only  used  in  special  cases.  In 
scores  where  figuring  is  used,  the  words  "  taste  solo"  is  often  found, 
which  indicates  that  the  organ-point  only  is  to  be  played. 


r44 


MANUAL    OF  HARMONY. 


CHAPTER   XIV. 


PASSING    NOTES  :     CHANGING    NOTES. 

Among  tones  foreign  to  the  harmony  are  especially  to  be  included 
passing  and  changing  notes. 

Passing  notes  result  from  inserting  tones  between  the  greater  or 
smaller  intervals  of  the  harmony. 

b. 


% 


J^^i^ 


m 


m 


The  notes  marked  ^  are  the  passing  notes^  those  marked  o  are  har- 
monic by-tones.,  that  is,  in  so  far  as  we  take  the  first  note  as  belonging 
to  the  triad  of  C  ,  or  a,  e.  g. 


246. 


( 


r 


r 


m 


pt3 


The  passing  notes  under  a,  Ex.  245,  are  called  diatonic^  those 
under  ^,  chromatic. 

Passing  notes  lead  from  one  harmonic  note  to  another,  and  cannot, 
therefore,  appear  on  the  entrance  of  a  chord  but  after  it,  upon  smaller 
parts  of  the  measure,  and  progress  onl}^  by  degrees. 

Changing  notes  are  those  tones  foreign  to  the  harmony  which 
appear,  like  the  suspension  or  appoggiatura.,  at  the  entrance  of  the 
harmony  (in  this  sense  on  the  accented  part  of  the  measure),  and 
join  themselves  to  the  harmonic  note  (No.  247,  (?),  or,  like  passing 
notes  on  the  unaccented  part  of  the  measure,  serve  as  a  melodic  embel- 
lishment of  two  notes  of  like  pitch.      (247,   b.) 


MANUAL  OF  HARMONY. 


HS 


©J-p^^ 


Changing  notes.,  therefore.,  may  enter  by  skips,  but  must  be  closely 
joined  to  the  har?nonic  note.,  as  shown  in  Ex.  247. 

That  changing  notes  can  be  formed  by  the  note  lying  below  as  well 
as  the  one  above.,  may  be  seen  from  the  above  example.  The  chang- 
ing note  below  the  harmonic  note,  especially  if  it  occurs  on  the  accent, 
inclines  naturally,  like  the  appoggiatura,  to  form  a  ?ninor  second  to 
the  principal  note,  giving  rise  thereby  to  chromatic  tones,  as  may  be 
seen  from  No.  247 ;  consequently,  passages  like  the  following  would 
be  objectionable : 


i±i 


*  * 


J- 


^ 


This  is  especially  the  case  with  changing  notes  which  are  introduced 
by  skips. 

When  they  follow  each  other  by  degrees,  as  in  a  scale  passage,  they 
assume  more  the  character  of  passing  notes,  and  the  following  passage 
of  changing  notes  at  <7,  need  not  of  necessity  be  written,  as  at  b: 


24-9. 


TX^-.  ^-.  ^-.  ^-. 

Those  changing  notes  below  which  do  not  fall  upon  the  accent,  do 
not  always  require  the  minor  second.  Thus,  Ex.  250,  «,  need  not  be 
written  like  /;,  but  c,  is  not  as  good  as  at  d. 


250. 


r 


r 


It  is  impossible  to  give  definite  rules  on  this  point,  nor  are  they  nec- 
essary, as  every  musical  ear  can  ascertain  that  which  is  right. 


Remark. — The  third  of  the  triad  admits  of  the  changing  note  taking  a  whole-step 
better  than  the  fifth  or  octave.  As  the  changing  note  before  (under)  the  octave  may 
also  appear  as  the  seventh,  the  harmonic  progression  only  can  decide  respecting  it. 


1^6 


MANUAL  OF  HARMONY. 


Changing  notes  above  the  harmonic  note,  whether  they  enter  by 
skips,  or  as  in  No.  250,  may  form  either  major  or  minor  seconds  to 
the  chord  note  because  they  occur  diatonically,  and  are  therefore  gov- 
erned by  the  key  and  moduUition. 


Changing  notes,  one  after  the  other,   above  and  below  the  chord 
note,  are  often  used,  e.  g. 


.r^ 


This  is  the  origin  of  the  following  much  used  embellishment : 

C5    I 


i^ggg 


T— P 


Passing  and  changing  notes  may  occur  in  any  of  the  voices.  If,  by 
preference,  this  takes  place  in  but  07ie  voice,  this  one  will  assume  a 
more  prominent  character,  while  the  others  will  serve  as  an  accom- 
paniment ;  or,  if  desired,  all  the  voices  can  be  made  to  participate  alter- 
nately and  thereby  gain  in  importance.  As  a  general  rule,  whenever 
the  position  and  progression  of  a  voice  will  admit  of  it,  the  applica- 
tion of  these  help-tones  will  give  it  greater  melodic  importance,  but 
here  again  there  must  be  a  limit,  as  too  much  development  in  all  the 
voices  at  once  will  produce  confusion  and  lack  of  clearness. 

The  following  simple  movement. 


254, 


# 


i^=^ 


-i-l 


-^- 


MANUAL  OF  HARMONY. 


H7 


^ 


e 


:^^ 


1 


A 


lA. 


I 


=F=F 


by  tlie  use  of  these  help-tones,  might  be  written  thus  : 


255. 


^^^^^mm- 


as3K 


^•^^Epgj 


t=t: 


=^E 


^ 


J=d=d^d=3: 


t=i 


;^] 


\  I 


iJt-j- 


-««.- 


^ 


The  passing  and  changing  notes  are  here  marked  by  crosses.  How 
easily  such  a  passage  may  be  made  to  suffer  from  the  addition  of  so 
many  tones  foreign  to  the  harmony,  may  be  seen  if  the  above  example 
be  played  in  a  somewhat  rapid  tempo.  This  style  of  writing  is  better 
adapted  to  slow  movements. 

The  same  rule  that  applies  to  suspensions  holds  good  here — the  har- 
mony note  following  a  changing  note  must  not  appear  in  any  other 
voice.,  e.  g. 


* 


g: 


t 


This  can  only  take  place  when  the  parts  are  distant  from  each  other 
at  least  an  octave,  c.  g. 


^E^d^Ehp^ 


*= 


MANUAL  OF  HARMONY. 


In  accordance  with  the  principles  of  doubling,  the  fundamental  or  fifth 
is  better  for  the  purpose  than  the  third  of  the  chord. 

In  quick  movements  and  with  more  lengthy  application  of  figures 
formed  by  changing  notes,  other  questions  will  arise,  as  will  be  seen 
from  the  following  passage,  which,  however,  cannot  be  taken  as  a 
four- voiced  vocal  phrase  : 


f 


As  to  the  regular  passing  notes,  the  same  rule  is  to  be  observed 
regarding  their  proximity  to  harmonic  tones,  and  figures  like  No.  259, 
a,  (5,  are  not  so  pure  as  c,  (/,  e. 


Here,  also,  more  rapid  figures  make  this  proximity  more  tolerable. 


260., 


i 


^TW 


^^ 


^-^-  •^ 


=F=i= 


I 


Faulty  Progressions  through  Connection  with  Passing  and 
Changing  Notes. 

As  passing  notes  are  used  to  fill  up  the  intervals  where  skips  are 
made  in  the  harmonic  progression,  care  must  be  taken  when  the  har- 
mony changes,  that  no  false  progressions  arise  through  covered  fifths 
being  changed  to  open  fifths  by  the  leading  of  the  passing  notes : 


J- 


P 


4 


^m 


261. 


-^^*i 


r— f 


MANUAL    OF  HARMONY. 


[49 


Open  octaves,  formed  by  passing  tones,  may  not  occur,  because  the 
first  of  them  will  be  harmonic  as  well  as  the  second. 


262. 


^I^i^ 


In  the  following  cases,  however,  the  passing  notes  will  not  cover 
the  open  octaves,  and  are  therefore  faulty : 


263. 


^^  -•-    I      r     I      -•- 


The  entrance  or  progression  of  the  changing  note  in  parallel  motion 

will  also  be  faultv  if  it  occurs  in  the  following  manner : 

better. 


The    last    example    is    better,   because    the    octave    progression  is 
covered. 

Passing  and  Changing  Notes  in  more  than  one  Voice  at  Once. 

Parallel  movements  of  thirds  and  sixths  are  most  effective  for  pass- 
ing notes  in  several  voices  at  the  same  time,  e.  g. 


265. 


'50 


MANUAL  OF  HARMONY. 


The  free  movement  of  the  voices  with  the  use  of  passing  notes  may 
also  give  rise  to  parallel  seconds,  fourths,  fifths,  and  sevenths,  of  all 
kinds,  and  require  great  care  in  their  treatment,  and  on  account  of 
their  harshness  are  only  to  be  admitted  singly  and  in  very  favorable 
positions.  Progressions  of  fourths  are  allowed  when  another  voice  is 
added  a  third  below  : 


266. 


33^ 


Single  fifth-progressions,  caused  by  passing  notes,  are  sometimes 
found  in  good  compositions,  but  that  is  no  reason  why  they  should  be 
regarded  as  faultless.  In  the  same  way  the  harshness  of  seventh-suc- 
cessions can  only  be  modified  by  a  favorable  position,  a  good  pro- 
gression of  the  voices,  and  through  tempo,  movement,  etc. 

In  contrary  motion.,  the  various  intervals  of  the  passing  notes  often 
give  the  passage  a  peculiar  coloring,  and  add  materially  to  the  inde- 
pendence of  the  voices,  but  they  should  not  appear  too  plentifully  or 
in  too  many  voices  at  once. 


:ffi3 


1^^ 


267. 


Here  also  it  will  be  seen,  that  those  passing  notes  which,  in  con- 
nection with  others  lying  beyond  the  simple  harmonic  structure,  form 
a  new  (passing)  harmonic  leading,  are  smoother  and  more  natural 
than  those  whose  formation  cannot  be  explained  harmonically.  The 
value  of  such  movements  can  only  be  arrived  at  by  taking  into  con- 
sideration their  character  and  tempo. 

In  regular  harmonic  progressions,  several  voices  may  receive  pass- 
ing tones  simultaneously,  e.  g. 


^^^^mm\ 


268. 


MANUAL  OF  HARMONY. 


151 


In  all  such  passages,  the  main  point  is  whether,  at  the  change  of 
the  harmony.,  the  voices  shall  be  in  a  position  to  admit  of  their  form- 
ing a  regular  progression.  Changing  notes  can  occur  in  different 
voices. 

a.     In  txvo  voices  : 

In  parallel  motion. 


•« 


I 


3^^ 


td^^^l^^^^^ 


In  contrary  motion. 


f 


^i 


:^l-i 


•LJi 


I    I  bJ   J     M 


Tf^ 


=R^ 


i^' 


<5.      In  ////'i'c  voices 
271. 


In/c 


c.     in  /oz^r  voices. 


ip^ 


Remark. — Most  of  the  above  examples  may  be  taken  as  harmonic  progressions  over 
an  organ-point. 

It  is  plain  from  these  examples,  that  in  the  parallel  movement  of 
two  voices  in  changing  notes,  the  progressions  in  thirds  and  sixths  are 
the  most  natural,  while  parallel  seconds,  fourths,  fifths  and  sevenths 
always  produce  a  very  harsh  effect.  Thus,  no  one  would  be  apt  to 
call  changing  notes  like  the  following,  good : 


Good.    —  — 


273. 


i 


^l^s^^ 


i± 


& 


f^ 


m 


r-r^ 


rife 


i 


JC2  MANUAL    OF  HARMONY. 

Chano-ing  notes  may  also  be  of  greater  duration  than  the  harmonic 
note  which  follows  them,  e.  g. 

I 


274. 


-^^^ 


--^.,^^^&,^^ 


:8<±^ 


The  importance  in  composition  of  the  subjects  explained  in  Chap- 
ters XII,  XIII,  and  XIV,  is  sufficiently  great  to  warrant  a  careful  in- 
vestigation of  them,  as  a  thorough  knowledge  of  them  will  assist  ma- 
terially in  understanding  the  inner  harmonic  structure.  It  still  remains 
to  speak  of  their  relation  to  the  pure  harmonic  structure,  the  object  of 
our  next  studies. 

Since  the  term  "pure  harmonic  structure"  has  only  been  spoken  of 
generally,  it  will  be  necessary  to  examine  the  question  more  closely 
and  to  present  it  somewhat  in  this  manner : 

What  application  does  our  exercises  in  pure  part-ivriting  allonv 
us  to  make  of  these  materials  for  composition  ? 

It  is  undeniable  that  these  materials  are  particularly  adapted  for 
the  development  and  embellishment  of  the  voices. 

If,  however,  our  immediate  task  be  to  recognize  and  work  out 
simple  harmonic  formations^  then  everything  which  is  adapted  to  de- 
veloping the  voices  may  be  used ;  but  whatever  serves  for  embellish- 
ment only,  must  be  rejected ;  in  short,  the  essential  must  be  distin- 
guished from  the  unessential. 

First,  as  unessential,  must  always  be  classed : 

All  unnatural  and  unusual  hartnotiies  in  general^  zvhere  they  are 
not  founded  upon  an  imter  necessity. 

Thev  may  easily  cause  overloading  and  confusion  in  a  passage,  and 
give  evidence  of  a  disordered  or  weak  mental  condition  rather  than 
strong,  original  work ;  next. 

Irregular  introduction  ofsuspe?zsions;  the  use  of  sustained  voices,, 

and  anticipated  and  delayed,  or  after-struck  tones ;  and  especially 

The  changing  notes  which  enter  free,   and  the  figures  formed 

frofn  them,  in  short,  whatever  is  not  appropriate  to  a  good,  plain 

four-voiced  song. 

Vocal  composition  being  generally  regarded  as  the  basis  upon 
which  all  music  is  founded,  much  will  have  to  be  excluded  which 
properly  belongs  to  instrumental  works.      If    the    use  of  chorals  or 


MANUAL    OF  HARMONY.  1^2 

movements  in  that  style  is  suggested  for  practice  in  learning  a  good 
and  pure  leading  of  the  voices,  yet,  even  this  will  not  exclude  the  use 
of  those  materials  when  they  serve  not  only  for  ornament,  but  for 
developing  the  leading  of  the  voices. 

Especially  to  be  reckoned  among  these,  is  the  use  of  suspensions 
and  the  regular  passing  and  changing  notes. 

From  the  foregoing,  it  may  now  be  understood  that  much  which 
was  forbidden  as  immaterial  and  not  to  the  purpose  in  connection  with 
the  first  study  of  the  pure  harmonic  structure,  may  still  be  readily 
used  in  practice,  whenever  favorable  opportunities  present  themselves. 

A  complete  understanding  of  the  subjects  so  far  discussed  will  be 
greatly  facilitated  by  studying  good  compositions.  We  shall  return 
to  this  subject  in  Chapter  XIX,  when  opportunity  will  be  afforded 
for  attempts  of  our  own. 


CHAPTER   XV. 

PASSING    CHORDS. 

Passing  chords  are  those  which  appear  in  the  weaker  parts  of  the 
measure,  like  passing  notes  in  several  parts,  and  which  sometimes 
deviate  from  the  general  rules  of  chord-connection.  One  variety  has 
appeared  already  in  those  passing  and  changing  notes  in  three  voices, 
which  assume  the  form  of  a  chord,  e.  g.  in  Nos.  271  and  272.  So 
that  in  one  sense,  the  chords  formed  over  an  organ-point  may  be 
called  passing  chords.  There  are,  however,  still  other  phenomena 
of  the  sort  which  must  be  explained. 

As  passing  and  changing  notes  generally  depend  upon  rhythmical 
conditions,  it  becomes  necessary  for  the  explanation  of  passing  chords, 
to  glance  at  the  different  divisions  of  the  measure. 

It  is  known  that  in  simple  even  kinds  of  time.,  the  accent  naturally 
falls  upon  the  first  part  of  the  measure,  while  the  second  part  receives 
less  weight. 

Now,  if  the  harmonic  progression  be  based  upon  the  two  divisions 
of  the  measure,  the  harmonies  which  fall  upon  the  accented  part  will 


154 


MANUAL    OF  HARMONY. 


always  be  regarded  as  the  more  weighty  and  important,  and  as  the 
point  to  which  the  chords  of  the  second  part  will  lead : 
o  I  o  I 


275. 


m^^i 


T  ^  r 


mm. 


^ 


In  this  sense,  the  chords  on  the  second  half  of  the  measure  may  be 
called  passing  chords,  although  the  regularity  of  the  movement  some- 
what obscures  their  chai-acter. 

That  this  has  been  so  understood  in  theory,  if  not  plainly  expressed, 
is  shown  by  the  fact  that  much  more  care  has  always  been  given  to 
chords  which  appeared  on  the  accent,  and  much  allowed  to  those  on 
the  unaccented  part  which  was  not  permitted  to  those  on  the  accent. 

The  character  of  passing  chords,  however,  appears  more  clearly 
with  such  harmonies  as  appear  on  the  smaller  division  of  the  meas- 
ure, as  in  the  following  examples: 


m 


u 


u 


2      7b 


6 

4   7 


i±E 


=tf 


7b  8      --4   7 


277. 


* 


9i: 


gp 


The  peculiar  appearance  of  the  chord  of  the  sixth  and  fourth  in  Ex. 
276,  a  and  c,  and  also  of  the  chord  of  the  seventh  at  c,  is  only  to  be  ex- 
plained as  a  movement  of  all  the  voices  by  degrees,  in  the  manner  of 
passing  notes,  to  the  nearest  chord — that  on  the  accent  of  the  next 
measure. 


MANUAL    OF  HARMONY. 


^55 


These  voices  may  be  still  more  easily  identified  in  their  character  as 
passing  if  one  voice  remains  stationary,  for  example,  the  bass  of  No. 
277,  a,  or  the  upper  voices,  at  b. 

The  leading  of  the  voices  in  No.  276,  a,  arose  from  applying  both 
modes. 

If  this  condition  (the  progression  of  the  voices  by  degrees)  be  ful- 
filled, all  the  chords  can  enter  free,  and  find  their  explanation  in  the 
chord  which  next  succeeds  them. 

N.B.       _ 


J33 


ii 


Remark. — The  free  (upward)  leading  of  the  seventh,  before  mentioned,  is  here  jus- 
tified in  this  explanation  of  the  passing  chords. 

In  the  simple  tmeven  measure,  the  accent  will  also  fall  upon  the 
first  part  of  the  measure,  while  there  will  be  two  divisions  of  less 
weight.     Passing  chords  will  appear  thus  : 


279. 


Smaller  divisions  of  the  measure  can  also  contain  passing  chords,  but 
after  the  above  no  further  explanation  is  necessary.  Here,  also,  the 
study  of  good  compositions  will  be  advantageous.  The  following 
remarks  may  still  apply  for  personal  attempts : 

All  chords  denominated  as  passing,  will  either  progress  in  accord- 
ance with  the  known  rules  for  harmonic  progression,  or  deviate  from 
them.  In  the  first  case,  which  is  the  more  frequent,  nothing  further 
need  be  said ;  in  the  latter,  it  will  depend  upon  a  flowing,  melodious 
movement  of  the  voices,  individually,  as  well  as  in  relation  with  each 
other,  whether  formations  of  this  kind  are  to  be  considered  correct. 


156 


MANUAL    OF  HARMONY. 


It  can  only  be  observed  generally,  that  here  also  the  movement  of  the 
voices  by  degrees  ivill  determine  the  character  of  the  passing  chords^ 
and  that  all  such  passages  must  be  judged  with  reference  to  the  rhythm, 
tempo  and  character  of  the  piece. 


CHAPTER   XVI. 


THE    MEANS    FOR    MODULATION. 


The  term  modulation  has  already  been  explained  in  Chapter  XT. 
The  object  there  was  to  designate  each  modulation  correctly.  We 
have  now  to  treat  of  the  best  means  of  effecting  modulations. 

The  art  of  modulation  consists  in  finding  those  chords  which  are 
related  to  two  or  more  keys,  in  order  by  their  aid  to  pass  from  one 
key  to  another. 

Modulations  can  be  effected  in  many  ways,  and  serve  various 
purposes. 

Firstly,  they  may  appear  abruptly,  and  the  new  key  may  pass  away 
quickly;  or 

Secondly,  they  may  be  more  gradually  prepared,  in  which  case 
the  new  key  will  serve  for  some  time  as  the  foundation  for  the  har- 
monies employed. 

In  the  first  case  the  modulation  will  be  introduced  by  the  simplest 
and  quickest  means,  and  although  it  maybe  distinct  and  unmistakable, 
the  new  key  will  soon  be  abandoned  and  a  fresh  modulation  intro- 
duced. In  the  second  case  the  modulation  will  generally  be  gradu- 
ally prepared  bv  various  means,  and  the  new  key  will  remain  long 
enough  to  become  familiar  to  the  ear,  and  may  even  lead  to  a  cadence 
or  perfect  close.  Thus,  in  the  following  example,  the  modulations 
are  transitory,  and  the  key  changes  rapidly  without  wandering  far 
from  the  original  key  of  C  major : 

4 — ^__4 — 1_4__^_^'^_4 


280. 


153. 


(i±s 


n 


2 


i 


^r^^ 


i^ii 


C:     F:Yi 


G:  V7 


^^^ 


iE^t 


V7 


MANUAL    OF  HARMONY. 


157 


This  kind  of  modulation  is  only  suitable  for  the  more  nearly  related 
keys. 

In  the  next  example  the  more  distant  key  of  El2  is  gradually  ap- 
proached, and  when  it  is  reached  the  original  key  is  entirely  aban- 
doned. It  will  be  seen  how  the  transitory  modulations  are  employed 
as  means  of  introducing  the  final  modulation  into  Et?,  which  is  the  ob- 
ject of  the  phrase  : 


281 


e 


:S: 


±1 


:^:^ 


^S 


^=^=i^ 


:&# 


ll] 


iiE 


.b»- 


ss 


^ 


-^ 


^^* 


±21 


C:  I  b\>:  VII07  B\)-l  /:  V7         E\):    V7 


Unless  these  short  passages  are  employed  as  interludes  between  two 
compositions  in  different  keys,  or  as  exercises,  they  must  be  made  use 
of  in  a  prescribed  manner,  since  upon  this  formation  of  modulation 
rests  also  that  of  the  periods  and  their  divisions.  This,  however,  is 
an  important  part  of  the  doctrine  of  form,  and  is  foreign  to  our  present 
purpose. 

We  take  at  present  the  formation  of  such  modulations  as  exercises, 
in  order  to  develop  skill  in  the  use  of  harmonies  and  their  proper 
connection. 

In  considering  the  means  by  which  modulations  are  effected,  it  will 
not  be  necessary  to  distinguish  between  the  above  two  methods,  since 
the  same  will  serve  for  both  kinds. 

The  first  and  most  simple  means  of  modulation  will  be  the  tOnic 
triad  of  the  new  key  itself.  If  this  triad  is  identical  with  one  of  the 
chords  of  the  original  key,  it  will  only  require  the  dominant  harmony 
of  the  new  ke}'  to  make  the  modulation  complete.  Thus,  in  the  fol- 
lowing example  at  a,  no  modulation  will  be  perceived,  while  at  ^,  the 
key  of  G  major  is  only  recognized  when  the  third  chord  is  heard : 


282. 


^i|i*Ei; 


"TTgFZ 


In  the  case  of  remote  keys,  the  tonic  7)iinor  triad  is  certainly  more 
decided,  but  even  this  chord  requires  the  dominant  harmony  of  the  new 


1^8  MANUAL    OF  HARMONY, 

key  to  render  the  modulation  unmistakable  (at  a) .  The  major  triad 
of  the  new  key,  when  not  followed  by  its  own  dominant  harmony,  has 
in  itself  somewhat  the  effect  of  a  dominant  chord  (3). 


i 
1 


:j(^ 


I 


C:     I 


a:   V 


C:\ 


As  the  tonic  triad  used  as  above  for  modulation  shows  itself  to  be 
weak  and  unsatisfactory,  it  is  seldom  used  in  its  fundamental  position, 
but  its  second  inversion,  the  chord  of  the  sixth  and  fourth^  has  the 
property  of  rendering  the  modulation  particularly  decided.  In  this 
case  also,  the  tonic  triad  is  followed  by  the  dominant,  which  completes 
the  modulation,  and  at  the  same  time  forms  the  closing  cadence. 


284.' 


i^e^ 


C:lG:l 


=F=4^ 


:|^ 


I      V7 


If  this  chord  be  employed  on  the  unaccented  part  of  the  measure, 
the  modulation  will  not  be  so  decided  : 


i 


'  676 

-«-  4  «  4  « 


S: 


i^e 


7|j 


I 


MANUAL    OF  HARMONY. 


159 


A  still  more  effectual  means  of  modulation  is  the  domina7it  triad., 
and  especially  the  chord  of  the  dominant  seventh^  which  renders  the 
new  key  clear  and  unmistakable. 

According  to  the  principle  that  the  connection  of  chords,  one  with 
another,  is  best  effected  by  means  of  tones  belonging  to  two  succes- 
sive chords,  and  remaining  in  the  same  voice,  modulations  may  be 
formed  through  the  chord  of  the  dominant  seventh  from  the  chord  of 
the  tonic  of  the  original  key  to  any  other  key,  excepting  those  of  the 
minor  and  major  thirds  and  the  augmented  fourth. 

Thus,  from  the  key  of  C  major  into  all  keys  (whether  major  or 
minor  is  immaterial  at  present)  except  Eb,  E,  and  F^,  modulations 
may  be  formed  as  follows,  the  connection  being  in  each  case  observed 
by  means  of    tones  which  remain  stationary,    and   indicated   by  ties. 


286. 


i^-j^^ii=5-J^3^i=ll^^' 


Db:  Or:   ,  C        to         At>:  C        to        Bb: 


(2 t?i2_t-^_ 


'^=^'^^=^\l'^-' -y--- 


;-";— i?j 


^=*i^r^i^|r*^'-*-^^^^-#l-ir^4^ii 


It  is  obvious  that  these  modulations  may  be  made  in  various  posi- 
tions of  the  same  harmonies,  e.  g. 


--fegi^=iEPa^3 


In  order  to  modulate  into  the  remaining  three  keys  (Eb,  E,  Y^  an- 
other chord  will  be  required,  usually  a  triad,  which  will  supply  the 
needed  connection,  e.  ". 


From     C  to  Eb:        C  to  E:  C  to  Fj. 


— *«'-  -  -#^r- 


i6o 


MANUAL    OF  HARMONY. 


Similar  modulations  may  be  formed  from  the  minor,  as  follows. 

From     a  to  b\  a  to  d:  a  to  e: 


Into  the  remaining  keys  C,  Dj?,  Eb,  Fji  and  At?  through  a  connecting 
chord : 

From       a  to  C:  a  to  Db; 


290.^^^ 


gig 1 


-27- 


to  Ab: 


It  is  of  course  understood  that  the  above  examples  merely  show  the 
simplest  principle  of  modulation,  and  that  it  is  not  necessary  that 
modulations  should  always  be  carried  out  in  this  way.  Nor  is  the 
above  mentioned  connection  of  chords  alwavs  requisite,  as  will  be 
seen  by  the  following  example  : 

From    C  to  Eb;  C  to  ^:  a  to  C: 


Lfi=«: 


3: 


^-=|tfe 


5S^ 


% 


-g^ g 


The  student  is  here  recommended  to  write  out  modulations  from, 
and  to,  all  keys,  major  and  minor,  through  the  chord  of  the  new  tonic, 
or  the  dominant  seventh,  and  in  doing  so  to  employ  all  the  various 
positions  of  the  chords,  and  to  play  them  on  the  pianoforte  when 
written,  in  order  to  become  well  accjuainted  with  their  effect. 


MANUAL    OF  HARMONY.  l6l 

Another  equally  important  chord  with  the  chord  of  the  dominant 
seventh,  is  the  chord  of  the  diminished  seventh,  which  is  often  more 
peculiarly  suited  for  jHuposes  of  modulation  than  the  former,  especially 
in  those  cases  in  which  the  seventh  and  fundamental  of  the  dominant 
harmonv  would  be  obliged  to  enter  without  preparation.  The  fol- 
lowing examples  will  show  the  application  of  this  chord  to  modula- 
tion : 

From  C        to       Bb:  C       to        B :         C        to        d\  a        to       e\ 


Beside  this  simple  and  natural  use  of  the  chord,  especial  advantage 
in  modulation  may  be  taken  of  its  enharvionic  nature. 

The  following  chord,  being  wa-itten  with  different  notation,  will 
belong  to  foiir  different  keys,  although  the  sound  will  in  each  case 
be  the  same. 


%J^^^^i 


In  the  first  of  the  above  cases,  the  chord  belongs  toy  minor,  in  the 
second  to  d  minor,  in  the  third  to  b  minor,  and  in  the  fourth  of  a\i 
minor. 

Thus,  by  means  of  one  chord,  four  modulations  are  possible  : 

FromC        to       /:  C        to         </:  C  to  b:  C         to      dO: 

-^^— C7^-I^^— Jta — ■^-  -a      f/?       J^=^^toiH 


^ 


it 


Now,  since  all  the  chords  of  the  diminished  seventh  can  appear  in 
the  following  three  positions, 


•g 


and  each  of  them,  through  enharmonic  change,  may  belong  to  four 
keys,  modulations  are  possible  for  all  twelve  keys  in  minor,  and  in 
many  cases  to  the  twelve  in  major,  as  this  chord  can  often  be  substi- 
tuted for  the  chord  of  the  dominant  seventh  in  major. 

A  similar  capability  of  enharmonic  change  is  possessed,  though  not 
to  so  great  an  extent,  bv  the  chord  of  the  augmented  sixth  and  fifth. 


l62 


MANUAL    OF  HARMONY. 


The  resemblance  which  the  sound  of  this  chord  bears  to  that  of  the 
dominant  seventh, 


296. 


!fe 


permits  the  one  chord  to  be  substituted  for  the  other,  and  thus  certain 
modulations  may  be  effected,  e.  g. 

From  C    to    b:  ^''^J^^-  ,     , 


297. 


^^mm^^^im 


-^ 


C:  Vt  b:  11O7 


^:V7     d:n°i 


So  far  we  have  been  considering  the  means  of  modulating  quickly 
from  one  key  to  another.  Since,  however,  it  is  not  always  an  object 
to  modulate  as  quickly  as  possible,  the  following  will  be  a  useful 
exercise : 

To  modulate  from  one  key  into  the  other,  by  means  of  the  triads 
of  the  different  degrees  of  the  original  key. 

From  Cto  d  through  the  triad  of  the  third  degree : 


298. 


i 


W- 


g^ 


From  C  to  d  through  the  triad 

Of  the  fourth  degree. 


Of  the  fifth  degree. 


From  C  major  to  E  through  the  triad 

Of  the  second  degree.  Of  the  fourth  degree. 


300. 


:2?^ 


J-        -^     .1^ 


3 


^ 


-iBoL 


15??: 


^ 


MANUAL    OF  HARMONY.  163 

Of  the  fiftli  degree.  Of  the  sixth  degree.  Of  the  seventh  degree. 


-^— vr« 


'S>^- 


The  above  examples  will  be  sufficient  to  indicate  the  manner  in 
which  other  modulations  may  be  formed  according  to  the  same 
principles. 

Extension  of  the  Modulation  and  its  Completion  by  means  of 
the  Cadence. 

The  process  shown  above,  for  passing  from  one  key  into  another, 
was  founded  upon  the  simplest  and  most  natural  means.  If  we  wish 
to  form  a  longer  and  more  gradual  modulation  than  any  that  have 
hitherto  been  met  with,  the  same  means  will  be  employed,  but  not  in 
so  direct  a  manner.  That  is  to  say,  instead  ot  proceeding  to  the  new 
key  by  the  shortest  and  most  direct  means,  transitory  modulations 
will  be  used,  and  the  new  key  be  introduced  by  degrees,  and  when 
reached,  will  be,  as  it  were,  fixed  and  rendered  distinct  by  means  of 
the  cadence.  For  this  practice  we  can  form  for  ourselves  exercises 
of  the  following  kind  : 

Modulate  from  C  major  through  d  minor,  a  minor  and  G  major  to 
e  minor.      This  could  be  done  something  like  this : 

I       I        ^-^  1       I         1       ,         .       -       4_ 


-19 '$'- 


"I — r 


-1—4-^-4 


is 


:^ 


^F^*tf 


m^^^^^^m^^^^ 


C:  I  d:\nO„ 


a:  viiO„ 


^.- V, 


When  adding  the  cadence,  the  following  should  be  noted : 
If  the  final  modulation  he  effected  through  the  chord  of  the  sixth  and 
fourth  of  the  tonic  triad  of  the  new  key  (see  Ex.  284),  then  it  will  only 
require  to  be  followed  by  the  dominant  chord  to  complete  the  cadence, 


302 


i 


J 


264  MANUAL    OF  HARMONY. 

In  other  cases  the  extended  or  prepared  cadence  must  be  added  to 
the  modulation  in  order  to  confirm  the  key.  The  simplest  forms  of 
the  extended  cadence  are  I — V — I,  the  first  of  the  three  chords  being 
usually  in  the  form  of  a  chord  of  the  sixth  and  fourth,  and  11 — ^V — I, 
the  chord  on  the  second  degree  generally  appearing  as  a  chord  of  the 
sixth  or  sixth  and  fifth,  e.  g. 

,  In  other  positions. 


1 


iiE: 


s 


:i: 


33g 


\ 


-^ 


i 


In  other  positions. 


iSJ^ 


m 


§i: 


^^- 


t 


The  position  of  the  chords  forming  the  cadence  will  depend  upon 
that  of  the  last  chord  of  the  modulation  to  which  they  are  added. 
This  is  shown  in  connection  with  some  former  examples.  The  mod- 
ulation from  C  to  Et?  (No.  388),  closes  with  the  fifth  in  the  soprano- 
To  this  is  added  the  cadence  in  the  position  which  will  connect  nat- 
urally with  this  last  chord,  e.  g. 

From  C  to  Eb.  Cadence. 


304-. 


1^ 


%-- 


Ji: 


-P^; 


5^ 


'^ 


% 


fe 


i^ 


±^ 


6 

4b  7b 


^■^- 


$^ 


% 


±2: 


fi 


i 


MANUAL    OF  HARMONY. 


165 


The  following  modulation  from  C  to  a  in  No.  2S6,  would   require 
a  cadence  in  this  position. 


SOS. 


The  modulation  from  C  to  B  with  the  cadence  under  No.  303  b  : 
From  C  to  B.  Cadence. 


306.< 


Or  from  C  to  Dl2. 

-IS &,2. 


We  conclude  with  an  example  on  a  more  extended  plan : 

From  G  through  e  minor,        C  major,  and  i^  minor  to  AP  major.    Cadence. 


^^S: 


-gj 1^: 


--^^w<^- 


i==t. 


hi^zdn^. 


S^#^ 


^-     ^ 


The  above  will  give  an  idea  of  how  we  can  form  for  our.selves  a 
great  variety  of  exercises. 


i66 


MANUAL    OF  HARMONY. 


PART  III. 


THE   PRACTICAL   APPLICATION    OF   HARMONIES  — 

EXERCISES   FOR   THEIR   USE   IN   THE   PURE 

HARMONIC    STRUCTURE. 


The  following  hints  regarding  the  most  practicable  application  of 
harmonies,  will  serve  still  further  to  explain,  elaborate,  and  make 
more  complete  the  principles  thus  far  developed.  Individual  cases 
will  give  occasion  for  further  remarks. 


CHAPTER  XVII. 

THE    SIMPLE    HARMONIC    ACCOMPANIMENT    TO    A    GIVEN   VOICE. 

In  treating  of  the  harmonic  accompaniment  to  a  given  voice,  we 
have  to  consider  the  simple  melodic  progression  of  each  part,  and  all 
other  elements  of  a  melody,  such  as  metrical  and  rhythmical  varia- 
tions, will  remain  for  the  present  out  of  the  question. 

I.   Harmonic  accompaniment  of  a  soprano. 

The  following  simple  exercise  is  selected : 


309. 


"^ 


^E^- 


i 


The  letters  used  before  to  indicate  the  fundamental  tones  which  are 
to  serve  as  the  harmonic  basis,  will  be  added  above  : 

C  Q  Q,  d  G  <Z 


310. 


-^ 


^ 


In  every  harmonic  progression,  the  leadi?ig  of  the  bass  is  of  the 
first  importance. 


MANUAL    OF  HARMONY. 


167 

We  direct  our  attention,  therefore,  to  this  first,  which  according  to 
the  fundamentals  indicated  may  be  as  follows: 


31  1. 

^             C 

Ttr '^ 

G 

C 

d 

G 

& 

C 

—II 

Soprano. 

F* 

=H 

1^ 

^^ 

rs 

6 

6 

a 

n 

-^   \\j        <s 

1 

^ 

-H 

or  thus 


312. 


.^gt$^ 


;0 


The  addition  of  the  middle  voices  will  not  now  be  difficult : 
313.  C  G  C  d  G  C 

K     ^~~l= — ^ 1-=^      I      ^      I ,^-=n=z 

Soprano. 


Bass. 


— t^ — ^ — 

— «> — 

?> 

I ^ 

1 & 

"     <s 

— H 

^ 

\^\    /It '^ 

1 G 

1 (S? 

, a. 1 

1 <s— 

=1 

Si 

^ 

^ 

?> 

1 ^~ 

=H 

^•n^ 

6 

6 

& 

s> 

LI 

i-l 

rs 

=u 

The  above  will  serve,  for  the  present,  as  an  explanation  of  the  ex- 
ercises themselves. 

In  order  more  clearly  to  explain  the  principles  of  a  good  progres- 
sion both  of  the  bass  and  middle  voices,  we  shall  make  use  of  exam- 
ples incorrectly  worked  out. 


G7 


314. 


P 


G7 


i 


1 68 


MANUAL   OF  HARMONY. 


Remark. — For  the  sake  of  saving  space,  we  shall  use  the  violin  clef  in  the  follow- 
ing examples,  and  write  the  voices  together  on  two  staves.  The  pupil  is  advised, 
however,  for  personal  work  to  practice  the  method  used  in  No.  313. 


This  exercise  may  be  worked  out  thus  : 

C  F  G7  C  d 


W 

(a 


G7 


t 


The  above  example  contains  no  violation  of  any  of  the  rules  of  pro- 
gression or  chord-connection  hitherto  shown,  nevertheless,  it  is  meager 
on  account  of  the  stiffness,  weakness,  and  insecurity  of  the  bass. 

In  a  good  progression  of  the  bass  (except  in  case  of  an  organ-point), 
no  tone  must  remain  stationary  unless  it  is  required  to  do  so  in  order 
to  serve  as  the  preparation  of  some  dissonance,  or  unless  it  is  equal- 
ized and  counterbalanced  by  a  very  decided  movement  in  all  the  other 
voices. 

The  above  example  also  contains,  in  two  places,  a  faulty  use  of  the 
chord  of  the  sixth  a7td  fourth.,  ysA\\cX\  W\\\  afford  an  opportunity  to 
speak  of  the  employment  of  this  peculiar  and  difficult  chord. 


Of  the  Use  of  the  Chord  of  the  Sixth  and  Fourth. 

The  chord  of  the  sixth  and  fourth  (second  inversion  of  the  triad) 
is  far  less  frequently  met  with  than  either  the  fundamental  position 
or  the  first  inversion  of  the  chord.  The  reason  of  this  is  that  its 
proper  use  depends  upon  certain  conditions.  We  have  already  seen 
how  it  is  used  in  the  formation  of  the  cadence,  and  also  in  connection 
with  modulation,  where  its  effect  is  somewhat  similar.  In  both  these 
cases  it  may  enter  without  preparation,  but  always  on  the  accented 
part  of  the  measure  (thesis). 

Apart  from  these  uses  of  the  chord,  it  produces  the  best  effect  when 
placed  on  a  bass  which  either  remains  stationary  or  moves  by  degrees. 
In  this  case  it  should  be  an  inversion  of  either  the  tonic,  dominant,  or 
subdominant,  and  \is  fourth  should  be  prepared. 


MANUAL   OF  HARMONY 


169 


The  following  examples  show  the  application  : 


6  6 


\  6  6  66666  66 


In  the  above  examples,  the  chord  appears  most  naturally  when  rest- 
ing upon  the  three  primary  triads,  as  at  «,  while  upon  other  degrees 
(^)  it  easily  gives  rise  to  an  impression  of  modulation. 

If  used  on  the  unaccented  part  of  the  measure  (arsis)  it  may  appear 
under  the  same  conditions  as  in  the  above  examples,  and,  in  addition, 
may  be  used  with  the  bass  prepared  instead  of  the  fourth,  e.  g: 


317. 


f 


m^ 


I 


If  the  chord  of  the  sixth  and  fourth  appears  on  the  arsis,  it  must  be 
considered  as  a  passing"  chord,  if  on  the  thesis  it  will  have  the  char- 
acter of  a  suspension ;  its  effect  will,  however,  be  very  weak  if  intro- 
duced on  the  thesis  with  the  bass  prepared.  This  was  the  fault  in 
Ex.  315. 


318.' 


^zig: 


9- 


--^ 


ii^ 


i^i 


It  also  often  appears  as  a  real  suspension,  in  which  case  the  prep- 
aration of  the  fourth   is  fully  explained  and  justified;   in  the  second 


170 


MANUAL    OF  HARMONY. 


case  (at  a)  still  more  decidedly  on  account  of  its  appearing  with  the 
chord  on  the  third  degree,  which  occurs  so  rarely : 


319. 


i 

=1^ 

r 

1 

— H 

-2?- 

1 



31 

c: 

1  ^ 

6  ^ 
4 

3 

2 

6 
5 

^ 

-I-— 

6 

4 

6 
6 

=  1 

When  all  the  parts  proceed  by  degrees,  and  the  notes  are  of  short 
duration,  the  chord  of  the  sixth  and  fourth  may  enter  without 
preparation : 

\- 


W^ 


1 T 


n 


ii3 


a=F 


% 


i 


This  will  require  no  further  explanation  after  what  was  said  in  Chap- 
ter XV.,  regarding  passing  chords,  and  after  the  examples  276  and 
279. 

Remark. — The  fact  that  a  preparation  of  the  perfect  fourth  in  the  cliord  of  the  sixtb 
and  fourth  is  often  necessary  has  led  many  theorists  to  consider  the  interval  a  disso- 
nance. In  the  introduction  to  this  work  it  was  classed  among  the  consonances,  and 
the  grounds  for  this  view  were  stated.  The  necessity  for  preparation  is  only  felt  when 
the  fourth  occurs  between  an  upper  part  and  the  bass,  and  even  then  only  in  the  chord 
of  the  sixth  and  fourth,  for  the  chord  of  the  sixth,  fourth  and  third  may  often  appear 
without  preparation.  Occurring  between  two  upper  parts  the  fourth  is  as  free  in  its 
treatment  as  any  other  consonance,  while  this  is  never  the  case  with  a  dissonance, 
which  always  preserves  its  character  whatever  its  position. 


The  chord  of  the  sixth  and  fourth  derived  from  the  diminished 
triad  is  seldom  used  in  four-part  harmony  on  accoimt  of  its  incom- 
pleteness. 


821. 


f-=f 


9r 


MANUAL    OF  HARMONY. 


171 


In  the  three-part  phrase,  however,  it  may  he  used,  and  frequently 
supplies  the  place  of  the  chord  of  the  second.  (See  later,  the  three 
voiced  movement.) 

A  correct  and  pure  harmonic  progression  not  only  requires  that  the 
bass  shall  form  a  clear  and  intelligible  harmonic  foundation  to  the 
phrase,  but  also  that  each  voice  shall  proceed  according  to  certain 
melodic  rules. 

Certain  progressions  have  always  been  considered  unmelodious — 
among  them  two  consecutive  skips  of  a  fourth  or  a  fifth  in  the  same 
direction,   e.  ir. 


ii! 


The  above  are  improved  thus  : 


323. 


.9t 


I 


Even  skips  of  a  sixth  are  better  avoided,  and  the  progression 
altered  to  that  of  a  third  In  the  contrary  direction,  if  the  compass  of 
the  voices  admit  of  them  : 

Better.  _  Better. 


.^t 


I 


Progressions  of  atigmented  intervals  are  to  be  avoided  as  tin?)ielo' 
dious ;  diminished,  however,  are  allowable. 

Not.  ^  Better.  Not.  Better. 


1^ 


9i: 


* 


m 


-r 


The  skip  of  a  major  seventh  is  always  to  be  avoided,  that  of  the 
minor  seventh  onlv  in  case  of  an  inversion  of  the  same  chord,  but 
not  when  the  harmonv  changes. 


Not. 

_j2Z 


he 


326. 


1^2  MANUAL  OF  HARMONY. 

The  last,  in  something  like  the  following  progression  of  harmony; 

Not  very  good.  Not.  Not. 


j=gEgg|i§=teS33i;H 


j^ 


l^^l: 


^^ 


These  few  remarks  will  be  found  to  contain  the  principles  of  a 
good  melodic  progression,  and  will  suffice  for  the  present  simple  ex- 
ercises. It  must  be  observed  that  the  above  rules  of  melody  do  not 
refer  to  the  movement  of  the  bass  alone,  but  apply  in  general  to  that 
of  all  the  voices. 

Exercise  No.  314,  with  an  improved  progression  of  the  bass,  may 
be  written  as  follows  : 


328  a. 


i 


m^ 


iiEi 


Exercises. 


1. 

^ 

-I5>- 

^2 

2. 

1    r^ 

328  b. 

1,  V^ 

■  III 

\i/  '-' 

1^ 

II  U   ' 

ii3 

11 

J 

C       G         C 


F      C        G        C 


C        —      F 


^- 


fe 


-g     \e>     \^ 


-ig    I   <y— I— zy 


S 


G-      C 


G7     C  r/-         G  a  d.,       G7      C 


MANUAL    OF  HARMONY. 


173 


The  next  example  will  afford  an  opportunity  for  the  explanation  of 
an  important  and  difficult  part  of  harmonic  connection  and  voice 
leading. 


Exercise. 

/■o  C 


■g 


dt      Gn 


To  illustrate,  we  take  the  following  faulty  w'orking: 

Q  Y  b°  <Z  a  dl       G7 


fe 


iE$ 


0 


6  6  6  6  7 

5 

The  faults  in  the  above  example  are  three  in  number ;  firstly,  in 
doubling  the  third  of  the  chord  in  the  second  measure  without  reason, 
thereby  leading  this  and  the  following  harmony  into  an  awkward  po- 
sition ;  secondly,  the  progi'ession  of  covered  fifths  between  bass  and 
soprano  in  the  fourth  and  fifth  measures;  and  lastly,  the  entrance  of 
the  seventh  by  a  skip,  in  the  last  measure  but  one. 

With  regard  to  this  last  error,  it  has  already  been  stated,  that  the 
dominant  seventh  may  only  enter  free  when  the  fundamental  is  already 
present  in  the  preceding  chord  and  remains  in  the  same  voice ;  more- 
over, if  preparation  is  possible,  as  is  the  case  in  Ex.  330,  it  should 
always  be  observed. 


33 


,i 


m 


-j- 


^1 


9t 


-^ 


The  free  entrance  of  both  fundamental  and  seventh  is  less  harsh  in 
contrary  jnotion : 


174 


MANUAL  OF  HARMONY. 


in  parallel  motion.,  however,  It  is  always  to  be  avoided,  or  only  to 
be  used  in  very  favorable  progressions,  like  that,  perhaps,  in  the 
first  example  of  No.  333,  where  the  fundamental  (G)  is  already  pres- 
ent, but  in  another  voice. 


333. 


i 


The  first  of  the  above  mentioned  faults  will  be  corrected  later.  The 
second  and  most  important  fault  in  Ex.  330,  will  give  an  opportunity 
of  considering  more  fully  the  progression  of  covered  fifths  and 
octaves. 

Covered  fifths  and  octaves  occur,  when  two  voices.,  starting  frofn 
some  other  interval.,  progress  in  parallel  motion  to  an  octave  or 
fifth,  e.  g. 

Covered  fifths. 


Covered  octaves. 


|^3=ii3i=PlPPfi|g^ 


These  fifths  and  octaves  become  visible  if  the  skip  made  by  one  or 
both  of  the  voices  be  filled  up  by  the  intermediate  notes,  as  indicated 
above. 

Although  certain  covered  fifths  and  octaves  should  be  avoided,  yet 
if  such  progressions  were  entirely  excluded  from  the  four-part  phrase, 
the  choice  of  chords  would  become  extremely  limited,  and  the  pro- 
gression of  the  voices  very  much  restricted.  We  shall  therefore 
proceed  to  make  some  observations  on  the  employment  of  these  pro- 
gressions, although  positive  rules  which  would  apply  to  all  cases 
cannot  be  given. 

Covered  fifths  and  octaves  may  be  caused  by  various  kinds  of  pro- 
gressions ;  for  example :  one  voice  may  proceed  from  any  one  degree 
to  the  next  above  or  below  it,  while  the  other  voice  skips  a  greater 
or  less  distance  (in  which  case  the  skips  may  be  either  in  the  upper 
or  lower  voice)  ;  or  again,  both  voices  may  proceed  by  skips. 

In  either  case  the  covered  progressions  may  occur  between  the  outer 
voices,  between  the  middle  voices,  or  between  an  outer  and  a  middle 
voice. 


'IS 


MANUAL    OF  HARMONY. 

Covered  Fifths  and  Octaves  in  the  Outer  Voices. 

They  arc  julmissihle  if  the  upper  voice  progresses  by  a  step. 
Fifths. b^ c.    Octaves.  d.  e. 


:f 


335. 


^m 


^l^^ii^fagBgj 


At  the  same  time,  it  will  be  advisable  that  one  of  the  voices  be  led 
in  contrary  motion  or  remain  stationary,  as  at  a,  <5,  c.  Example  </, 
where  all  the  voices  move  in  parallel  motion,  is  not  so  good. 

Remark. — Although  the  above  rule  will  suffice  in  many  cases,  yet  it  will  not  always 
apply,  as  may  be  seen  at  e  in  the  above  example,  which  cannot  be  called  a  good  lead- 
ing of  the  voices,  as  the  progression  from  the  chord  of  the  sixth  is  a  very  forced  one. 
We  may  repeat  what  has  been  said  before,  that  the  progression  of  covered  octaves  in 
which  the  upper  part  moves  by  a  half-step  are  more  tolerable  than  those  which  pass 
over  a  whole-step. 

In  the  examples  shown  above,  it  will  be  observed  that  the  progres- 
sion is  always  towards  the  fundamental  of  the  chord.  All  those  cases 
where  the  progression  is  toward  the  third  should  be  avoided,  or  used 
with  great  caution.     For  example  : 

^  Not.  Not. 


336. 


Even  toward  t\\e.  JiftJi  of  the  chord  it  cannot  be  called  good. 


Remark. — In  case  of  the  covered  fifth,  the  lower  voice  will  always  be  the  funda- 
mental of  the  chord. 

Covered  fifths  between  the  outer  voices  are  to  be  avoided  ivhcn  the 
upper  voice  skips. 


338. 


^p^li^Pl^fej^^H 


176 


MANUAL    OF  HARMONY. 


Whenever  the  connection  is  made  closer  by  means  of  a  seventh,  a» 
at  3,  d^  <?,  in  the  above  example,  the  progression  of  fifths  appears 
more  covered  and  less  harsh. 

Covered  octaves  between  the  outer  voices  are  not  unconditionally 
prohibited  when  the  upper  voice  skips. 

b.  Not:  c.  d.    Not.  <..  | 


w^^ 


^ — fe^qi^gl 


f- 

6        ^: — .-^. 


B 


I 


Here  also  the  progressions  will  be  best  in  which  the  bass  moves  by 
a  half-step  only,  as  at  a.  The  remarks  made  on  Nos.  336  and  337 
will  apply  to  d  and  c. 

Covered  Jifths  and  octaves  between  the  outer  voices  are  to  be 
rejected  iv/ien  both  voices  skip. 


S4-0. 


i 


>Ei=E 


:[=^ 


i^izt 


IH^^feli^iH 


9^ 


i^^ 


^B^i:^i^ 


Such  progressions  are  not  faulty,  however,  when  they  only  form 
inversions  of  the  same  chord.,  because  in  that  case  they  do  not  pro- 
gress to  other  chords  which  Sive  fundamentally  different. 


34-1. 


(i 


j= 


^^S. 


;i 


9t 


m^^i\ 


Covered  Fifths  and  Octaves  in  the  Middle  Voices. 


Although  the  progression  of  the  middle  voices  ought  to  be  as  pure 
as  that  of  the  outer  voices,  yet  on  account  of  their  position,  being  as 
it  were  covered  by  the  outer  voices,  they  may  be  allowed  a  greater 


MANUAL    OF  JIARiMONY. 


77 


freedom  of  movement,  especially  with  regard  to  covered  fifths.  Hid- 
den octaves  between  the  middle  parts  are  seldom  good,  on  account  of 
the  voices  becoming  too  widely  separated ;  and  with  respect  to 
covered  fifths,  their  good  or  bad  effect  will  depend  on  the  good  con- 
nection of  the  chords  in  other  respects,  and  also  upon  their  agreement 
with  the  rules  relating  to  covered  fifths  between  the  outer  voices. 
A  few  cases  are  here  given  : 


l^g^^ 


( 

^    Not.                    Not.         ^ 

Covered  Fifths  and  Octaves  between  the  Outer  and 
Middle  Voices. 

Here  also  the  conditions  under  which  such  progressions  maj'  be  used 
cannot  be  determined  by  merely  mechanical  rules,  but  must  depend 
on  a  good  natural  connection  of  the  harmony.  The  following  are  a 
few  examples : 


±=gSS^^S3 


r    /n     r  ^^ 


H^ 


1^ 


Not  good. 


■■"■~^  g? 


"^^ 


■^-r^: 


i^g^p=r=g^i 


i 


178 


MANUAL  OF  HARMONY. 


One  peculiar  kind  of    covered  octave  has  still    to  be  mentioned, 
namely,  that  which  passes  over  the  seventh. 
This  progression  is  faulty  in  all  the  voices. 


(  See  Ex.  149  and  what  follows.) 

All  that  has  been  said  of  covered  octaves  applies  also  to  covered 
unisons.  These  are  forbidden  between  soprano,  alto,  and  tenor,  but 
may  occur  between  tenor  and  bass,  where  they  are  to  be  treated  as 
covered  octaves  —  according  to  the  position  of  the  chord  and  of  the 
voices  themselves. 

The  cases  in  which  covered  fifths  and  octaves  may  appear  are  so 
numerous,  that  it  would  be  impossible,  even  if  it  were  not  useless,  to 
cite  them  all.  The  above  remarks  may  be  sufiicient,  if  we  add  the 
following  maxim,  which,  however,  is  not  for  those  beginners  who 
are  still  engaged  with  the  technical,  or  purely  mechanical  harmonic 
structure,  without  regard  to  the  higher  requirements  of  art : 

Avoid,  indeed,  covered  fifths  and  octaves  whenever  possible ;  but 
regard  them  as  permissible,  where,  on  the  one  hand,  an  otherwise 
natural,  good  connection  of  harmony  is  obtained,  or  on  the  other, 
reasons  of  a  higher  order  prevail,  such  as  melodious  movement  of  the 
voices,  employment  of  given  motives,  etc. 

After  this  digression,  we  return  to  No.  330,  in  order  to  correct  the 
faults  it  contains. 

The  covered  fifth  found  there,  which  belongs  to  that  class  where 
both  voices  skip,  can  scarcely  be  remedied,  since  if  we  lead  the  bass 
in  contary  motion,  the  same  fault  will  appear  in  another  place,  though 
it   will    be    less    perceptible  on  account  of    its  occurring  between  a 


middle  and  an  outer  voice  instead  of   between  the  outer  v 


oices,   e.  g. 


MANUAL   OF  HARMONY, 


179 


In  such  a  case,  therefore,  we  have  no  choice  but  to  alter  the  har- 
mony itself,  and  select  a  different  marking  of  the  fundamental  tones, 
thus : 

C  F  <50  C  —  </7       G7  C 


1 


Ptf: 


t=t: 


s 


-&-  tS*- 


t  T 


ia 


^^ 


Or  thus : 


84-7  a. 


C  F 


^^=^ 


C  dt       Qi  C 


4=i 


-,5'-  -«'- 


ii$^ 


-S- f2- 


V=t 


Exercises. 


S: 


*- 


-^—~^- 


^ 


F  Bb        F         Bb         ^o        F  a'       ^^^        C7         F 


=6/1.    ^~ 

1 

,    a 

_::^_ 

-    '^ 

— 5?- 

— 

r— <g- 

— 

/y 

^— II 

3. 

1 — fin — '^ — 

- 

c 

^ 

c 
— «> — 1 

F 

c 

■^ 

5^   . 

C 

II 

F 

II 

— -^j 

— 





— t^i— 

-5^ 

li-^ 

^       F 
4.  ^. 

Bb 

g 

^ 

Bb          C7          F          ^7        C7        F 

—^ 

— iS* — 

_^c 

J 

~^' 

■  - 

--(5' — 1 — «>— 

=S=J 

4^ ' 

— 

' — 

FC^C^^F^^C^F 


[8o 


MANUAL  OF  HARMONY. 


The  following  exercise 


we  will  work  out  thus 
1. 


349. 


The  faults  of  the  above  have  been  numbered  for  reference. 

The  movement  of  the  three  upper  parts  by  skips  in  paralled  motion 
at  No.  I,  is  not  good,  since  it  deviates  from  all  the  rules  of  harmonic 
connection,  and  moreover  is  not  necessary. 

The  progression  of  one  or  two  voices  by  skips  is  only  allowable 
when  some  other  voice  preserves  the  harmonic  connection  by  remain- 
ino-  stationary  or  by  moving  in  the  contrary  direction. 

No.  2  has  the  same  fault,  and  is  made  still  harsher  by  the  free 
entrance  of  both  fundamental  and  seventh,  coming  thereby  in  an  awk- 
ward position  where  one  crowds  the  other. 

It  has  already  been  said,  that  either  the  dominant  seventh  or  the 
fundamental  ought  to  be  prepared. 

Thus,  all  of  the  following  examples  are  defective  : 

,  ^ I'jiSl^i^i^^ 

350. 


If  the  free  entrance  of  the  fundamental  and  seventh  takes  place  in 
contrary  motion,  the  effect,  as  already  stated,  is  less  unpleasant,  e.  g. 


MANUAL  OF  HARMONY. 


i8i 


Example  No.  349  also  contains  another  fault  at  No.  2,  namely,  a 
skip  in  the  bass^Vow  the  chord  of  the  sixth  and  fourth,  which  is 
contrary  to  rule. 

The  third  fault  in  Ex.  349  lies  in  the  covered  fifth  which  appears 
between  tenor  and  alto,  and  which  is  made  more  apparent  by  the  skip 
in  the  soprano. 

The  covered  fifth  at  No.  4  is  objectionable,  because  unnecessary; 
that  at  No.  5  is  better  on  account  of  both  alto  and  bass  moving  in 
contrary  motion  with  tenor  and  soprano. 

The  following  will  be  a  more  correct  working  of  Exercise  348  : 


352  a. 


352  b.^ 


G       C 


Exercises. 

G       -        D 


D7      G 


f 


i* 


D7 


I 


^ 


s* 


D7        G 


-laizt-^i 


i 


^ 


m 


.a,      -^- 


i 


,82  MANUAL  OF  HARMONY. 

The  next  exercise, 


m 


353. 


E7 


a        /J07       B7         e 


with  the  following  treatment : 


contains  an  incorrect  progression  known  by  the  nam^e  of  unharmonic 
cross-relation,  or  false  relation. 

The  tmharmonic  cross-relation^  which  belongs  to  the  unmelodious 
progressions,  occurs  when  any  tone  is  immediately  followed  by  the 
same  tone  chromatically  altered  in  another  voice,  as  in  the  second 
and  third  measures  of  the  above  example,  where  the  G  in  the  alto  is 
immediately  followed  by  the  Q\  in  the  bass. 

In  order  to  avoid  this  fault,  the  following  rule  must  be  observed : 
,  When  any  tone  is  to  be  immediately  followed  by  the  same  tone 
chromatically  raised  or  lowered,  such  chromatic  alteration  must  take 
place  in  one  and  the  same  voice. 

Although  this  rule  is  perfectly  consistent  with  all  the  theoretical 
principles  of  harmony,  there  is  perhaps  none  which  admits  of  so 
many  exceptions.  In  consequence,  in  manuals  of  later  methods,  the 
doctrine  of  the  cross-relation  has  been  regarded  with  suspicion,  and 
instances  cited  in  which  the  unharmonic  cross-relations  occur  in  a  per- 
fectly natural  way,  without  ascertaining  the  reason  why  they  do  not 
sound  faulty. 

Here  are  a  few  that  do  not  have  a  bad  effect : 


355. 


T 


m 


MANUAL    OF  HARMONY. 


^83 


In  all  these  cases,  the  cross-relation  is  not  formed  by  essential  notes 
of  a  simple  harmonic  progression,  but  is  the  result  of  a  contraction., 
or  abridgment,  of  certain  natural  progressions  which,  had  they  been 
employed  in  their  complete  form,  would  not  have  agreed  with  the 
metrical  character  of  the  phrase.  Thus,  in  the  character  of  changing 
notes,  as  at  a,  ^,  g;  or  through  contraction,  as  at  <:,  (/,  £',/',  h. 

The  original  progressions,  by  the  contraction  of  which  the  above 
cross-relations  were  formed,  are  as  follows : 


Compare  these   examples  with   those  under  No.  355,  at  c,  </,  <?,  h. 

These  conditions,  under  which  the  cross-relation  is  allowable,  are, 
however,  absent  in  the  following  and  similar  examples,  which  are 
therefore  incorrect : 


357. 


i84 


MANUAL   OF  HARMONY. 


Freedom  in  the  use  of  all  cross-relations  cannot,  therefore,  be  justified. 
There  is  also  to  be  taken  into  consideration  the  tempo,  the  consistency 
of  a  whole  resulting  from  rhythmical  divisions,  which  will  make  these 
formations  not  unpleasant,  but  rather,  precise. 

With  the  cross-relations  is  also  classed  a  progression  known  as  the 
tritone,  an  explanation  of  which  follows : 

The  tritone  is  contained  in  the  diatonic  major  scale  between  the 
fourth  and  seventh  degrees,  and  is  the  progression  of  an  augmented 
fourth,  in  the  key  of  C,  from  F  to  B.  This  interval  embraces  three 
U'hole  degrees^  and  derives  its  name  from  that  fact. 


358.  -^ 


ir 


Like  all  augmented  intervals,  the  tritone  should  be  avoided  on  ac- 
count of  the  difficulty  it  presents  to  the  singer.  This  difficulty  is 
doubtless  caused  by  the  fact,  that  each  of  the  two  tones  composing  it 
require  different  progressions : 

359. 

of  which  one  must  be  omitted  if  the  interval  be  given  to  one  voice; 
360. 


m 


unless  the  melody  be  formed  thus 


'^ 


That  this  is,  however,  not  the  only  reason  of  the  unpleasant  effect 
of  the  augmented  fourth,  is  proved  by  its  inversion,  the  diminished 
fifth,  which  would  also  require  a  two-fold  resolution,  but  which  is 
constantly  used  in  its  melodic  form, 


I 


and  is  just  as  pleasing  and  easy  of  execution  as  the  tritone  is  difficult 
and  disagreeable. 


MANUAL    OF  HARMONY. 


185 


Remark.  —  It  may  be  further  remarked  in  this  connection,  that  the  tritone  is 
founded  upon  the  diminished  triad  and  its  progression,  as  becomes  clear  from  Ex. 
362  above.     ( See  page  39.) 

The  reason  why  the  tritone  has  always  been  specially  prohibited  is 
that  it  was  the  only  augmented  interval  which  occurred  in  the  simple 
harmonic  progressions  formerly  in  use.  At  the  present  time,  how- 
ever, it  is  merely  classed  with  the  other  augmented  progressions,  which 
in  pure  part-writing  should  be  avoided  as  unmelodious,  or  at  least  to 
be  used  with  the  greatest  caution. 

There  are  two  things  to  be  considered  in  the  use  of  the  tritone. 
If  its  progression  is  caused  by  an  alteration  of  the  position  of  one  and 
the  same  chords  as  at  a  in  the  following  example,  its  appearance  is 
not  so  unexpected,  and  its  effect  much  less  unpleasant  than  when  the 
notes  of  which  it  is  composed  belong  to  two  different  chords^  as  at  3, 
where  the  forced  progression  is  perceptably  felt : 


Formerly  the  prohibition  of  the  tritone  was  extended  to  the  pro- 
gression of  two  consecutive  major  thirds^  separated  by  the  interval  of 
a  -whole  step,  e.  g. 


364. 


and  It  cannot  be  denied  that  in  two  parts  this  progression  has  the 
same  unpleasant  effect  as  the  tritone  itself.  In  three  or  four  parts, 
however,  it  is  considerably  less  harsh,  especially  when  it  is  not  heard 
in  the  outer  voices. 


[86 


MANUAL    OF  HARMONY. 


We  now  return  to  Ex.  No.  353,  in  order  to  correct  the  cross-rela- 
tion it  contains : 


I 


% 


i%^ 


1^ 


6  6 

5 


Exercises. 


i^ 


366  b.  E5-5 


e; 


» 


fc 


fc 


P^ 


r/«o 


B7 


B7 


g^  /u    g*- 


^S= 


D?  ^ 


D7 


2.      IIarmo?iic  accompafiitnetit  to  a  given  middle  voice. 

This  exercise,  which  properly  belongs  to  the  study  of  counterpoint, 
is  very  useful,  and  cannot  be  begun  too  soon.  As  in  the  preceding 
examples,  the  fundamentals  are  indicated  by  means  of  letters. 


Alto  C 


Exercise. 

CFG 


di  G 


s 


--m^ 


In  working  out  this  exercise,  the  progression  of  the  bass  will,  as 


MANUAL    OF  HARMONY.  1S7 

usual,  be  the  most  important,  and  should  be  considered  first;    at  the 
same  time,  however,  the  soprano  may  be  added,  e.  g. 


368.  < 


g 

^"- 

— <s> ■ 

F  ^    1  ^ 

\=\ 

E^3 

"^ 

=^=H 

»^ 

"^ — 

G 

L-^ — 1 
c 

F 

G 

a 

a,      G 

1= 

— (S- 

—a. — 

rs 

1— S' 

L^-  \ 

y=i 

^— fl 

The  foregoing  is  complete  as  a  three-voiced  movement ;   with  the 
addition  of  the  tenor  it  will  appear  thus : 


369  a. 


w 


-jS 1 i2- 


:s-Jizt=2^ 


i 


I  I 


m 


Exercises  with  given  Alto. 


1. 

369b.-|l^^-<|^^:^ 

^ 

~<9— 



I  ^ 

r-^ 

^        C7         ^         ^^        C         F 


F        Bij     C 


-mr^ — ~—^=^-^ — ^ — ^l-t^TTT^ — ^^ — ^ — ^--- 

hlj^t?                                                                          |-|^^i2iU                                                ^  _| 

B|?         C 


F         ^  C  F 

4. 


Il^jii 


F  C 


F        C      a- 


-<&— I — <5^ 


^         C        F 
5.       _ 


C        At       rt'         <^       A7     </ 


*fc« 


I 


€%  A 


*3S 


:|~?=r4^ 


:1N: 


D  — T 


BI2 


g  D7 


58  MANUAL    OF  HARMONY. 

A  given  tenor  will  be  similarly  treated: 
Exercise. 

Tenor.  C  G  a  F  C  G?         C 


M 


t 


Sketch  of  the  bass  and  soprano  : 


371.< 


i 


1: 


;b 


i±t 


For  four  voices 


372  a.' 


:^r 


1=:^ 


m\ 


i±aE^ 


^: 


-^-      -^- 


Exercises  with  given  Tenor. 


-f -Ttr-^ —--^ ^ ^ ^^ ^-^-  I^^TtT-^— ^- 

■     1^  (|/                                                                  ^         '^                    "  (|/ 

C          G7         C         G          a          fl'        G7      C 

C         G 

ESE 


C         G7        C 
4. 


i|^ 


i 


a  E7         «  ad         g^^       a  —         l^         Yji         a 

These  exercises  should  be  continued  until  the  sketching  of  the  bass, 
as  well  as  the  leading  of  all  the  other  voices,  is  perfectly  pure  and 
free. 

In  closing  this  chapter,  it  may  be  observed  that  in  order  to  form  a 
good  four-voiced  movement,  a  good  position  of  the  parts  is  indispens- 
able. The  compass  of  the  voices  must  not  be  exceeded,  the  distance 
between  the  voices  must  not  be  too  great,  neither  must  it  be  too  small. 


MANUAL    OF  HARMONY. 


189 


The  following  rule  should  be  observed : 

The  distance  between  any  two  of  the  three  upper  voices  7mist  never 
exceed  an  octave.      Between  the  bass  and  tenor  there  are  exceptions. 


CHAPTER    XVIII. 


Extension  ok  the  iiakmonic  accompaniment. 

To  a  given  voice  in  whole  notes,  with  the  harmonic  accompani- 
ment in  half  notes  alternately  in  the  other  voices.  This  can  be  done 
through  two  chords,  through  change  of  position  in  one  chord.,  or 
through    suspensions.     The  exercises  will   be    marked    the  same  as 

before. 

Exercises. 


373. 


Y—1      b^Gl 


G7 


;b 


IE 


The  bass  may  be  sketched  in  this  manner 


^r-^ 

1 

^— 

1 i 

-^w 

2 

6         7 

2 

6 

_^ —~- 

8        7 

u 
— ^^fl 

^  \|/    fy 

-^'r^ 

k=^=^ 

-t=i_t= 

t^-^ 

1 

:-^=EI 

Secondary  chords  of  the  seventh  appear  'witho?it  preparation  in  the 
second  and  fourth  measures.  These  are  called  passifig  sevenths. 
They  start  from  the  fundamental  of  the  chord  and  always  occur  upon 
the  arsis.     In  this  way  they  are  admissible  in  all  the  voices. 

By  adding  the  middle  voices  to  the  above  sketch,  we  get  the  follow- 
ing four-voiced  movement. 


375, 


i 


I 


f=f' 


s 


r^ 


jCZ. 


iH 


190 


MANUAL    OF  HARMONY. 


The  same  exercises  with  richer  harmony  may  be  like  this 
C  F/«07         G  ^«07      aQih        dT>  G— 7 


376. 


•M= 


Worked  out 


377. 


'.31 


111 


f=r 


^^ 


:^=^ 


\     ?   \     \ 


^ 


iA 


f=T 


:0 


6  75  7  4,       6         -         8        7 

3b 

The  next  exercise  will  exhibit  the  application  of  suspensions. 

F         Bb  C  ^  p-  F  Bb        C7  F 


378 


^gi$EE 


;[| 


Worked  out : 


We  pass  over  the  exercises  in  the  middle  voices. 

The  object  in  using  the  simply  melodic  progression  in  whole  notes 
for  exercises  {cantus  Jirmus)  was  to  show  the  simple  harmonic  con- 
tents of  a  measure,  or,  if  in  Alla-breve  time,  its  principal  divisions — 
half  notes. 

If  the  exercise  is  to  be  in  half-notes,  chorals  may  be  used  for  the 
purpose.  For  individual  practice,  the  fundamentals  of  well  harmo- 
nized chorals  may  be  taken  of,  as  shown  below,  and  the  working  out 
attempted  as  follows : 


MANUAL  OF  HARMONY. 
Kt      d       a    di  IPl     E       E 


191 


E    -7 


380. 


S: 


rpj: 


-f9- 


Sie 


•<s— F 


^-=^ 


t=i4=l= 


^ 


G      C         F      ^o      C    F      C 


E?: 


:^=t 


C7b   d      — 


S3^ 


«/«° 


:t==1: 


-^ — z?^- 


Efe 


i 


G  —  7        CG         «7DG        CG 


^^7     G  E  a 


^ 


SEig 


As  above  indicated,  this  choral  could  be  worked  out  thus ; 


-xa ia 1 — &. /^. 


^  -19- 


rr- 


§3E=f 


■-^t 


f- 


i 


f-r 


t=d: 


*     s- 


I      1 


?i 


u 


I    I 


^i^ 


ipp 


r— r 


1 


fr^F=f 


r— r 


=«F 


r 


:eee 


■i    J 


i 


9fc 


1 


?■    r 


d^=Eis 


:#^ 


I 


I 


193 


MANUAL  OF  HARMONY. 


After  sufficient  practice  has  been  had  to  insure  certainty  in  the  treat- 
ment of  simple  harmony,  we  can  proceed  to  the  further  development 
of  the  voices  through  passing  and  changing  notes.  For  this  purpose, 
melody  and  melodic  progression  will  be  further  treated  in  the  next 
chapter. 


CHAPTER   XIX. 


ON  THE  FORMATION  OF  MELODY. 


The  inventio7t  of  melody  will  not  be  discussed  here,  but  its  devel- 
opment, and,  what  is  of  great  importance  for  our  harmonic  exercises, 
to  learn  and  to  know  how  to  use  that  which  is  essentially  harmonic  in 
the  formation  and  treatment  of  melodies.  Everything  will  depend 
upon  the  recognition  and  comprehension  of  the  following  principles  : 

Every  melody,  however  fully  developed  it  may  be,  has  a  foundation 
just  as  simple  as  the  examples  we  have  used  in  our  previous  studies. 

Therefore,  every  harmonic  leading  of  the  voices,  no  matter  how 
complicated,  can  be  reduced  back  to  a  simple  connection  of  harmony. 

To  fully  appreciate  this,  it  will  be  necessary  to  learn  how  to  dis- 
criminate between  the  essential  and  that  which  is  used  as  auxiliary  or 
ornamental. 

We  select  for  this  purpose  the  analytic  method,  and  will  attempt  to 
develop  the  following  melody,  given  in  its  simplest  form,  according 
to  the  method  used  before,  with  indication  of  the  fundamental  tones. 


332. 


^■7f-fe7tT->5- 

1 

^S"— 

rr\ 

Ir      ^. 

— 

Bb 

F 

Bo 

^ 

C 

F 

d 

F 

C7 

F 

Both  melody  and  harmony  are  simple,  and  the  latter  may  be  written 
out  for  four  voices,  thus  : 


"mt- 

n 

«>■ 

«-     ■" 

G> 

^ 

_^s? 

V     ^ — 1 

ry 

b a. 

-i5>- 

U2- 

jS- 

9^^?}F= 

— f — 

i G> 1 

& 



0 

G> 

1 ^ ~l 

MANUAL    OF  HARMONY. 


193 


Before  proceeding  to  further  develop  this  movement,  it  will  be 
necessary  to  premise  what  is  to  be  mentioned  concerning  the  rhyth- 
mical formation  of  a  melody. 

A  melody  may  be  either  a  musical  movement  containing  more  or 
less  measures,  without  any  fixed  limit,  as  often  occurs  with  themes  or 
motives  of  a  composition,  or  it  can  be  a  distinct  whole,  separated  and 
bounded  by  antitheses. 

In  the  latter  case  it  is  called  a  period,  and  contains  usually  eight 
measures,  which,  divided  into  two  sections  of  four  measures  each, 
form  antitheses.  These  sections  are  often  called  "thesis  and  antithe- 
ses"— sometimes  "  antecedent  and  consequent." 

That  the  above  movement  forms  a  period  is  evident  from  the 
close  at  the  end.  It  will  next  be  in  order  to  ascertain  the  divisions 
into  sections.  These  points  of  division  are  very  often  marked  by  the 
cadences  which  occur  in  the  middle  of  the  passage,  either  as  imperfect 
whole,  half,  or  plagal  cadences.  Such  a  half -cadence.,  usually  a  close 
on  the  dominant,  occurs  in  our  exercise  at  the  sixth  and  seventh  meas- 
ures, and  the  point  of  division  between  the  two  sections  of  the  period 
will  be  at  the  place  where  the  sign  f  stands. 

The  first  section,  the  thesis,  will  therefore  contain  seven^  the  anti- 
thesis six  measures,  and  each  must  be  rhythmically  changed  to  four 
measures.     This  may  be  effected  in  the  following  manner  : 


•=P§^ 


;@ 


By  adding  the  harmonic  accompaniment  selected  above,  a  complete 
musical  period  is  obtained. 


194 


MANUAL  OF  HARMONY. 


Transformations  into  different  kinds  of  time,  as  for  example,  into  |, 
I,  I,  or  i  time,  are  very  easily  managed,  e.  g. 


•is 


3t::* 


g^f?^fg^g^ 


is 


'=^f=^=B 


S^Ji^^^p^  '-i^^^l^^Ei 


We  come  next  to  the  tonic  variations  of  the  melody,  and  add  to  it 
passing  and  changing  notes,  e.  g. 


386.  E^gt|t^=5y|p^^g^p|ir=J_^t^ 


tq 


3^=^=^l 


-• hs* 


A  still  freer  use  of   all  auxiliary  tones  could  give  the   following 

form  :  ^ ^ 

Adagio. 


MANUAL   OF  HARMONY.  ,gc 

The  simple  melodic  progression  underneath  is  easily  recognized  as 
the  original  foundation.  It  will  be  evident,  if  we  add  the  other 
voices,  with  the  few  deviations  made  necessary  by  the  upper  voice, 
tnat  the  above  melody  is  carried  out  with  reference  to  the  original 
harmony : 

Adagio.  ....^--^     , — ^  'TI     ^    rn^^  S 


^m%^m 


iii 


5±* 


tf 


— rP 


i    i 


?=^ 


I 


sSSeSi^^ 


As  to  the  parallel  octaves  in  the  middle  voices  in  the  third 
measure  of  this  example,  they  may  be  regarded  as  faultless  when  they 
do  not  occur  singly,  but  in  longer  passages  as  a  doubling  of  another 
voice  for  the  purpose  of  giving  it  greater  prominence.  In  this  case 
the  movement  would  be  regarded  as  three-voiced. 

Notwithstanding  the  small  independent  worth  of  this  example,  it 
has  served  to  show  how-  the  simplest  melodic  and  harmonic  movement 
can  be  developed. 

The  advantage  to  be  derived  from  studying  and  recognizing  these 
melodic  and  harmonic  relations  is  too  great  for  us  to  refrain  from 
giving  another  example  in  the  following  interesting  movement.  The 
fundamental  harmonic  progression  is  just  as  simple  as  in  the  previous 
example. 


389. 


if=&feH 


i-^fe* 


I 


This  passage  forms  a  period.      The  middle  close  is  found  in  the 
half -cadence  in  the  seventh  measure. 


T96 


MANUAL  OF  HARMONY. 


We  omit  the  different  kinds  of  measure,  and  select  the  following 
section : 


390, 


.    J.  i    =* 


S§i^^^.-^^mga 


The  upper  voice  may  be  developed  in  the  following  manner,  at  the 
same  time  adhering  to  the  harmonic  progression. 


The  following   passage  from    Beethoven's  El?  major  quartet  will 
show  how  the  other  voices  can  take  part  in  melodic   development: 


392. 

ViOLINO  I. 


ViOLINO  II. 


Viola. 


Violoncello. 


^3^^nrv^x^ 


w. 


3^3=^ 


:r-5=?: 


J -J- 


i^ flai • 


§te! 


EE?E^ 


lf^=*=*^3 


MANUAL  OF  HARMONY. 


197 


A  comparison  with  No.  390  will  show  the  melodic  and  harmonic 
variations. 

Here  follows  still  another  variation  of  the  original  melody  from 
the  same  composition : 


393, 


fc^= 


^^S^p^pi^^^^^ 


The  other  voices  aj^pear  with  the  following  variations. 
394. 


sa 


P^^^ii^^Pg 


r^: 


•^- 


iiS! 


^ 
i^^ 


l2ziiS 


^ 


^ 


P 


gJ 


These  hints  regarding  the  development  of  melody  will  be  sufhcient 
here,  while  further  practice  may  be  left  to  the  personal  efforts  of  the 
student. 


Remark.  —  The  mechanical  character  of  this  whole  treatment  should  not  mislead 
us;  for  certainly  in  composition  one  does  not  always  proceed  in  the  way  shown  above. 
Our  only  object  here  was,  partly,  to  place  in  the  right  light  the  relation  of  our  pre- 
vious exercises  to  the  practical  side,  and  partly,  to  gain  a  clear  insight  into  complicated 
compositions  themselves. 

Concerning  the  accompanying  voices,  they  arose  naturally  from 
the  simpler  harmonizing  and  required  little  change,  showing  them- 
selves, even  if  subordinate,  yet  not  unimportant  on  that  account. 
Other  kinds  of  accompaniment  will  be  spoken  of   in  the  next  chapter. 


198 


MANUAL  OF  HARMONY. 


CHAPTER   XX. 

ON    DEVELOPMENT    OF    THE    ACCOMPANYING    VOICES. 

The  manner  in  which  the  voices  take  part  in  harmonic,  metrical  and 
melodic  development  has  been  shown  in  the  previous  chapter.  There 
are,  however,  still  other  styles  of  accomjDaniment,  known  as  the 
figured  accompaniment.  It  is  not  adapted  to  the  character  of  the  vocal 
parts,  and  its  use  is  therefore  very  limited.  In  the  following  inves- 
tigation, instrumental  music  only  will  be  discussed. 

By  figured  accompaniment  is  understood  that  kind  which  arises 
through  metrically  uniform  transformations  of  the  simple  chord 
tones,  e.  g. 


Simple  harmony.     Figured  accompaniment. 


;=^ 


^ 


'V^ 


-9—\ •—\ •- 


rroLf-D-^-^^^-ti 


i 


^ 


i=5=F^ 


^=S=^=f?=^?=f 


fSf^E^ 


-^x 


^^^    ^^'  ^S^  '^      !    I    I    ^-^—     L_^i    ^^ 


The  accompaniment  at  a  is  tiarmonically  figured.  These  figures 
are  also  called  broken  chords.  That  at  b  is  metrically  figured,  and 
that  at  c  is  melodically  figured.  These  last  are  formed  from  chang- 
ing and  passing  notes. 

Any  accompanying  voice  can  be  used  for  such  figuration,  either 
alone  or  with  the  other  voices. 

We  select  the  beginning  of  No.  382  for  an  attempt  in  some  kinds 
of  accompaniment.      The  following  remarks  may  be  presented  : 

When  the  figures  are   uniformly  repeated,   for  example,  in  broken 


MANUAL  OF  HARMONY. 


r99 


chords,  all  the  rules  for  the  leading  of  the  voices  must  be  observed  at 
the  change  of  chords^  as  v^^ell  as  in  doubling. 
We  must  not  write  : 


396. 


but  somewhat  in  this  manner  : 


^Sl^l 


f p-^ 


Or. 


^P^^L 


^W=^^ 


^-^- 


i 


When  the  harmony  changes,    the  last  note  of  one  figure   and    the 
first  of   the   next   must   not  form  a  false  progression  with   an}-  other 


voice,  e.  g. 

Not. 


Not  better. 


EEEIEE3 


Harmonic  figuration  enables  us  to  form  one-voiced  movef?ients  more 
perfectly.     The  examples  may  begin  thus: 

A., 


;!§ 


si 


One  voiced. 

N 


^t=± 


^ 


^^ig^ 


i^^ifei^as^iiiiiii 


It  is  evident  that  these  movements  are  suitable  for  an  instrument 
like  a  violin  or  clarionet. 


MANUAL  OF  HARMONY. 


Three  voiced. 
In  the  middle  voice 


In  the  lower  voice. 


In  the  upper  voice. 


3 


w^^ 


i±, 


gj^a^ggg^-,f^ 


In  two  voices. 


MANUAL    OF  HARMONY. 


Figuration    in  the   four-voiced    phrase,  will   be  an   easy  task    after 
these  attempts  with  the  above  example. 

We  prefer,  instead,  to  quote  an  example  of  varied   figuring   from 
the  quartet  bv  Beethoven,  mentioned  above. 
401. 


^|^^?^^"^^=F^^=^^=^=JVt-,: 


'-hE3^=\ 


I 


^ 


pizz 


ftE?i^ 


^^Np^^^P^ 


iife 


l^g;  q    ^1^-4,^    j!    ^^^-g— g; 


s^ 


iJs^gS^=E^^g=i^45— ^-q     ^^  -F^ 


MANUAL    OF  HARMONY. 


g^;^j^^^t:;g^aggfe^g^^^^E^ 


Wr- 


1 


^ 


S^ 


SS^E 


1^ 


F- 


TJ? 


i 


The  whole  of  this  rich  development  rests  on  the  harmonic  hasis 
given  in  Nos.  390,  391  and  392  ;  and  in  every  case  where  the  harmony 
changes  the  leading  of  the  voices  is  carefully  ol^served. 

If  a  clear  insight  into  such  elaborate  compositions,  and  a  comphre- 
hension  of  their  inner  harmonic  structure  is  desired,  it  will  be  very 
useful  to  reduce  works  of  this  kind  back  to  their  simple  harmonic 
basis. 


CHAPTER   XXI. 


THE    EXERCISES    IN    THREE-VOICED    MOVEMENT. 


With  few  exceptions,  our  exercises  thus  far  have  been  written  in  the 
four-voiced  form,  and  although  it  affords  greater  completeness,  and 
seems  best  adapted  for  harmonic  connections,  the  three-voiced  move- 
ments are  also  of  great  value,  being  particularly  adapted  for  greater 
skill  and  freedom  in  the  leading  of  the  voices. 

We  begin  as  before,  with  exercises  witli  figured  l:)asses. 


■i!* 


-^ 


l==t 


6    6 
6    4 


^P^ 


^i 


e=5^ 


1^ 


^ 


MANUAL    OF  HARMONY. 


203 


The  three-part  phrase  is  sufficient  for  the  triad,  but  through  the 
leading  of  the  voices  one  of  its  intervals  may  sometimes  be  wanting. 
In  the  case  of  the  seventh  chords,  one  interval,  of  course,  will  always 
be  lacking,  but  this  must  never  be  the  seventh  itself.  As  a  rule,  the 
fifth  can  be  omitted,  as  was  the  case  with  four  parts,  and  also  in  many 
cases  the  fundamental  also,  but  the  third,  the  interval  which  determines 
the  nature  of  tlie  chord,  can  seldom  be  omitted  without  causing  an 
especial  vagueness.  The  exercise  will  be  as  follows,  to  which  we 
append  a  few  remarks  : 


4-03. 


N.B.5 


N.B.6 


(^       r- 

l- 

<5> 

v~r^ — '^^T!^ — r — 1 

I'/U         f3          ?> 

1        r 

<3 

■         \         \         \ 

1|3         1 

11^-^.7^-^ "                         ^                           '               ' 

-* — -v^f—r- 

-(2 <9— 

-tt^ — \ — 

-H \ 

1 ^ — 

7876,64            $4           6                    62 

rv-    1     ,r?     1^ 

1 

1 

^  \}\'    \       \ 

« 

v^    ^ 

8    N.B. 

9 

10 

11 

_ 

12 

F~T7 — ^ 

II 

Vr-x. 

1               1 

-^ 

^^— H 

H^,^— -|2 • \ 

^-(2. — 
-1 

-f- 1 

FF= 

-f^- 

■^ 
--P- 

-^ — n 

li^— 1 1 

4 
6             3 

^^: — 1 1 

'                1 
6 

—^ ^-^ 

_J 1 

6 

-A 

6 
6 

— 1= 

: U 

H 

-^-^ — 5 — 

1 

S 

'T^ 

-J— 

0     . 

^=^\ 

In  the  fourth  measure,  at  N.  B.,  the  chord  of  the  sixth  and  fourth 
of  the  diminished  triad,  E — G — Bb,  appears.  It  takes  the  place  of  the 
chord  of  the  second,  Bt? — C — E — G,  the  fundamental  of  which  is  here 
omitted.     For  four  voices  the  chord  would  appear  thus  : 


i 


p 


■^w- 


i 


See  pages  170,  and  171,  concerning  this  chord. 


204 


MANUAL   OF  HARMONY. 


In  the  fifth  measure,  a  fourth  represents  the  chord. 

While  a  fourth  can  neither  in  three-part  nor  in  two-part  writing 
supply  the  place  of  a  full  chord,  as  is  the  case  with  the  third  or  sixth, 
yet,  in  those  cases  where  the  chord  of  the  sixth  and  fourth  can  be  used 
in  four-part  harmony  as  a  passing  chord  on  the  arsis,  in  three  parts, 
in  order  to  secure  a  better  leading  of  the  voices,  the  sixth  (third  of  fun- 
damental chord)  can  be  omitted,  leaving  the  fourth  alone  to  represent 
the  fundamental  and  fifth  of  the  original  chord. 

In  two-part  movements,  the  fourth  will  sometimes  stand  instead  of 
the  chord  of  the  second,  especially  in  the  case  of  a  passing  seventh,  e.g. 
\  I 


w 


4  4 

With  four  parts,  the  above  place  in  Ex.  403  would  stand  thus : 


i^ 


P 


I 


In  Ex.  403,  eighth  measure,  the  chord  of  the  sixth  and  fourth  is 
formed  complete  through  the  skip  in  the  alto. 

In  the  tenth  measure  appears  a  chord  of  the  sixth  and  fifth,  which 
is  really  a  suspension  of  the  fourth,  which  by  the  movement  of  the 
bass  resolvas  into  a  third.     This  appears  plainer  in  four  parts  : 


407. 


The  last  measure  of  No.  403  shows,  through  the  octave  F,  that  the 
triad  can  appear  in  such  cases  even  without  the  third  and  fifth. 

That  the  leading  of  the  voices  will  often  cause  the  omission  of  the 
third  is  shown  in  the  first  and  second  measure  of  the  next  example. 


MANUAL   OF  HARMONY. 

X 


205 


-\f^^- 

■~1 

— (2_ 

1"^      r^ 

_h2 s^ 

^— 



hi 1= 

1 

1 

rzp ^: 

p„ii4j; 

6 

6 

— 1 

J \ — 

6 

4             t 

7              5 
4 

'                      1 

3               6B 

2S:i=t= 

^= 

^M 

The  omission  of  the  third  occurs  best  upon  the  arsis,  as  here  on  the 
third  beat  of  the  measure,  but  it  must  never  be  lacking  on  the  accent, 
or  thesis. 

Further  exercises  may  be  left  to  the  teacher. 

Exercises  in  the  Three-voiced  Movement  to  a  Given 
Upper  Voice. 

The  following  exercise,  with  the  fundamentals  indicated,  is  to  be 
worked  out  for  three  voices  : 

C  G  C  —  F  a  d  (]7  C 

-^-        -^-        -^-_^-  


The  above  needs  no  explanation. 


2o6 


MANUAL    OF  HARMONY. 


The  choice  of  the  middle  and  lower  voices  will  generally  depend 
upon  the  position  of  the  chords.  Thus,  in  a  low  position  the  tenor 
would  be  more  suitable  than  the  alto ;  so,  also,  can  the  tenor  be  taken 
as  the  lower  voice  instead  of  the  bass. 

The  tenor  is  selected  as  the  middle  voice  in  the  following  example, 
as  its  movement  clings  more  to  the  bass,  while  the  simple  song  of  the 
soprano  seems  more  isolated. 

The  former  exercise,  with  a  more  extended  development  of  the 
harmony : 

Qa      d    G       Ert       GC       dgto^      a  e        ^  D  G7  C 


4ii.==S: 


^- 


412. 

Treatment. 


¥■ 


» 


^^=F^ 


I 


-^--^- 


iiiES 


6  ^      "f 

-«-     -(2- 


-6?-f2- 


^^^rf='^^f=f^f^ 


■P=t: 


N.B. 


In  the  fifth  measure,  at  N.  B.,  a  real  ninth  suspension  appears, 
through  the  position  of  the  voices,  as  a  second,  and  which  can  occur 
hut  seldom,  and  only  between  tenor  and  bass.  It  may  here  be 
remarked  that  there  cannot  be  a  second-suspension,  because  the  sec- 
ond results  from  the  inversion  of  the  seventh  and  must  conform  to  the 
resolution  of  the  latter,  e.  g. 

Or:  Inversion. 


^^■ 


E 


I 


r 


41 


Exercise  in  a  middle  voice. 
Tenor.        a'        A        Bb        C 


geO 


^«o. 


H 


MANUAL    OF  HARMONY. 


207 


For  an  upper  voice,  the  alto  is  here  the  most  convenient. 
4-15. 


ttsr? 


i^: 


■«> a- 


i?g^^§^g 


^^H 


§£it 


416 


The  same  exercise  with  the  following  selection  of  chords : 

dg      A— ^   Bb  G    C  F   B»2  C^       ^    Bb  F      gC^    d        A        d 


•  g^ 


S 


417. 

Treatment. 

T-r^^ 

^f~ 

-f=-+^ 

^H^-^^ 

i^' 3.bt^_^ _J ! ^ \ 

-[-- ^-H — h— H ^ 1 

(fleft-^^— :i— 

^ 

^-'-^ 

e> 

g» 

1                 ^ 

7 

6 

pd= 

6 

-1— T= 

6 

1            r^i 

— t>^K-^    ^-^^ 

^^- 

-J— ^'- 

^^ 

i^=i 


SE 


^m 


PE 


|£ 


:H 


9- 


6 


^ 


?^ 


^;i 


The  last  measure  but  one  shows  that  even  the  sixth  can  form  a 
suspension. 

For  further  practice,  the  exercises  which  were  formerly  given  for 
the  four-voiced  movement  can  be  used. 


ao8 


MANUAL  OF  HARMONY. 


CHAPTER   XXII. 


ON    THE     TWO-VOICED    MOVEMENT. 


The  poverty  of  the  two-part  phrase  from  a  purely  harmonic  stand- 
point, makes  it  seldom  available  except  in  contrapuntal  labors,  where 
alone  it  derives  importance  from  being  applied  in  polyphonic  move- 
ments, for  example,  in  fugues.  If,  indeed,  for  simply  harmonic  use, 
a  metrical  and  rhythmical  variety  in  the  formation  of  the  voices  will 
make  the  two-voiced  movement  tolerable,  still,  the  contrapuntal 
development  of  the  two  voices  can  alone  free  them  from  the  monot- 
ony of  extended  progressions  of  thirds  and  sixths,  and  give  that  com- 
pleteness which  every  polyhonic  movement  must  possess. 

Necessarily,  the  omission  of  one  or  more  intervals  will  always  take 
place  in  this  movement.  With  the  triads,  it  will  usually  be  the  fifth 
or  the  fundamental.  When  chords  of  the  seventh  are  used,  of  course 
the  seventh  must  not  be  omitted.  Octaves  and  fifths  should  rarely  be 
introduced,  as  they  sound  too  empty.  The  fourth  can  only  be  used 
in  a  few  cases  where  the  chord  of  the  sixth  and  fourth  would  be 
admissible,  or  when  it  takes  the  place  of  the  chord  of  the  second. 
(See  page  203.) 


Example.    C 


b^ 


^ 


418. 


^^ 


419. 


( 

Treatment 

r  fy 

ii5) 

^  rj 

JZ. 

-^- 

p-^ 

r—<5> 

^^Fl 

5 

3 

6 



6 

3 

6 

6 

3 

<3 

3 

: II 

1 

1 

'A-x~l\i ' 

,.    s> 

--f5> — 1--^<&— 

G 

11 

[ 

n-a-*)^^— 



1 

II 

The  intervals  which  have  been  omitted  can  be  ascertained  by 
comparing  the  fundamental  tones  in  Ex.  418.  Lack  of  clearness  in 
the  harmony  will  be  rare,  since  each  chord  explains  itself  by  its  con- 


MANUAL  OF  HARMONY. 


209 


nection  with  the  one  which  precedes  and  follows  it.      The  same  exer- 
cise with  varied  harmony: 

C  F— 7        G  CG  d  CCaG  C 


G 

j2- 


420. 


"^ 


W- 


^1] 


^ 


m- 


-^^^ 


i 


p^= 


r-=Ff=F 


:|=p: 


P: 


t=t=1=|: 


Most  of  the  exercises  in  Part  III  invade,  somewhat,  the  domain  of 
counterpoint.  The  only  difference  is,  that  here,  the  harmonies  are 
indicated,  and  we  have  only  to  carry  out  the  leading  of  the  voices 
accordingly,  while  in  contrapuntal  studies,  a  knowledge  of  harmony 
and  facility  in  its  use  is  assumed,  so  that  the  selection  of  the  harmo- 
nies can  be  left  to  the  choice  of  the  student. 

These  studies  may,  therefore,  be  regarded  as  useful  preparatory 
exercises  to  those,  and  will  at  the  same  time  afford  an  insight  into  the 
relationship  between  harmony  and  counterpoint. 


CHAPTER   XXIII. 

HARMONIC    TREATMENT    OF    A    GIVEN    VOICE    IN    MELODIC    FORM. 

By  melodic  development  of  a  voice  is  not  to  be  understood  here 
that  richer  ornamentation  shown  in  Chapter  XIX.,  but  through  met- 
rical variety  to  avoid  the  simple  choral-like  progression  of  our  earlier 
exercises,  and  thereby  afford  opportunity  for  learning  to  develop  the 


MANUAL  OF  HARMONY. 


voices  better  in  the  harmonic  accompaniment  also.      The  next  exer- 
cise will  make  this  clearer  : 


422. 


^^- 


^^ 


a^^fi—^- 


-^-  ^.  ^. 


The  choice  of  chords  will  be  made  at  the  time  of  treatment.  Al- 
though the  kind  of  measure  chosen  will  of  itself  produce  a  similar 
melodic  leading  of  the  voices  to  be  filled  out,  still,  particular  attention 
must  be  given  to  their  leading  according  to  the  principles  developed 
in  the  previous  chapters,  if  a  free,  skillful  treatment  of  them  is  to  be 
had.      The  exercise  will  first  be  treated  in  three-part  harmony. 

423.  .^ 


P 


3: 


^- 


T=- 


;t==F 


-I — p 


e* 


'G>-r°- 


£ 


6        98 


9i«: 


6       6 
7     6       4      5 

^<5> 


:t=t^ 


This  treatment  needs  no  further  explanation  after  the  remarks  on 
the  three-voiced  movement. 

The  harmonic  treatment  of  this  melody  as  a  middle  voice  shows  its 
adaptability,  and  may  be  recommended  as  a  useful  exercise. 

To  retain  the  alto  voice  and  obtain  a  better  position  for  it  we  trans- 
pose the  melody  to  F  major. 


iii=_^S^ 


s=S^ 


^f= 


H=2__^_ 


4=1 


P=^= 


canlus  firmus. 


SH 


^-&- 


-f9^-i5>-    ^    -|22-    -|S2.-^. 


1=Ft 


g|^=£^ 


I 


6       6 
7       683       9846  6       987 


1^1 


'^^ 


The  explanation  of  the  unprepared  chord  of  the  sixth  and  fourth 


MANUAL    OF  HARMONY.  211 

in  the  fourth  measure,  is  found  in  tlie  remarks  on  passhig  chords  in 
Chapter  XV.  It  arose  accidentally,  on  account  of  the  progression  of 
the  bass  by  degrees,  and  stands  here  in  the  place  of  the  chord  of  the 
second. 

The  treatment  of  the  same  cantus jirtnus  transferred  to  the  bass  : 

425. 


This  treatment  shows  a  weak  point  from  the  third  to  the  fourth 
measure,  in  the  harmonizing  of  the  sustained  A  of  the  bass.  Also  the 
bare  fourth  in  the  sixth  measure  is  a  very  imperfect  representative  of 
a  chord,  unless  we  regard  it  as  a  passing  note. 

If  it  be  desirable  to  develop  the  leading  of  the  voices  still  further, 
passing  and  changing  notes  can  be  used  alternately  in  the  two  voices 
to  be  added,  e.  s^. 


T    c./. 

"^ 

'f' 

r>    e>  ' 

'^ 

1 

_ 

r^ 

^ 

' 

1 1        f\ 

''^'"    .^r-. 

\ r^* 

l{^-?^~f-[— ^p^h- 

-^ 

f    p\m    f    P    m^km    f 

[^_^PJ — : L_l_ 

k-r-hM— P-h^  F+ 

6 

6 

^7             6 

1 

m                ^    <y 

0     r     0             1       1  "1 

'  1.  fS                          r5 

T    m    P 

■ 

^     •     J 

^-^r^ P— 1 

-^-^p^^ 

_. __| 

-1       1       1 

T-^-^ 

^i 


9^^ 


t=A- 


=f=t=t 


=S 


=f=t 


?E^^ 


MANUAL   OF  HARMONY. 


The  remaining  treatment,  that  of  the  cantus  Jirmzis  in  the  middle 
voice,  is  here  given  : 
4-27. 


1^ 


#-^ 


"c- 1 W—i 


^ 


E^a= 


#-  • 


il=t 


F=^=^ 


c.f. 


^55 


'r     ^ 


§a^^ 


:iK 


6966 
— ^»-# 


^v- 


w=^ 


^  -0- 


:^=^=P=P4 


^:^J 


S 


-(2.  .(2.  ^. 


EEE^ 


i5 


Sii 


T=p= 


—1- 


^=1  I  I  ^=Mr^ 


As  examples  of    four-voiced    treatment,   the  following  may  serve 
here  : 


428.[-z||z^ 


^— ^- 


^2Jr-G>—[- 


^V=^=^ 


I 


4-29.     Four- voiced  treatment. 


pS 


-^  I  r^  g?  ^1      ^^'^.f^f—f^-r^ 


■t=F 


^a 


*E 


I 


» 


)=P=F 


fe^i^ 


IS 


N.B. 


:r!it 


&^^^^£S^ 


6 
4      3 


6      ' 
8  6  6       6-6 

67        43     55     543       867 


^m 


^^_^^Tp^ 


H 


'  n!b. 


MANUAL  OF  JJARMONY. 


213 


In  the  fifth  measure  at  N.  B.,  the  skip  of  the  tenor  into  the  seventh  is 
not  altogether  faultless,  because  the  soprano  skips  also  in  parallel 
motion  to  the  fundamental,  G.  This  can  only  be  excused  by  the  posi- 
tion of  the  alto,  which  holds  the  connecting  tone. 

In  the  same  measure,  appears  the  chord  of  the  sixth  and  fourth  of 
the  augmented  triad,  the  original  fifth  of  which  is  prepared.  It  has 
here  the  character  of  a  suspension  from  below.  (See  Suspensions, 
Chapter  XII.,  page  131.) 

The  same  cantus  Jirmus  in  the  alto,  transposed  to  D  major : 


te 


^^ 


N.B. 


:^£ 


te 


c.f. 


eee£ 


»=•! 


trfta 


-f3E^E^ 


iSl 


iM 


£ 


-^-      &- 


it* 


I 


S3: 


^^q?      J  — I- 


n 


-x=x 


Si 


In  the  fourth  measure  suspensions  are  found  in  three  voices.  In 
the  fifth  and  sixth  measures  the  position  of  the  alto  and  tenor  is  not 
good,  because  they  are  more  than  an  octave  apart. 


214 


MANUAL    OF  HARMONY. 


Of   the  remaining   treatments,  that  with  the  cantus  Jirmus   in  the 
bass  here  follows : 


-(2--&- 


an^ 


^^^-rrrTrr^^g^Sj 


* 


^^- 


fer^ 


at 


\^-f^\ 


I 


r?  <?  r?- 


fe 


t=4: 


t=f=C 


as 


C-./-  4      3 


6 

4 
6       2 


6      2       6    5 


-(2_«, 


6         3B 


-^-   -G- 


S£ 


SEE 


6       I 


I 


The  introduction  of  the  chord  of  the  seventh  of  the  seventh  degree 
in  the  fourth  measure,  lacks  clearness,  because  the  fundamental  lies 
immediately  above  the  seventh.  (See  page  76.)  Besides  this,  its 
progression  does  not  follow  here  according  to  the  movement  of  the 
leading  tone,  but  in  the  same  cadencing  form  as  with  other  seventh 
chords:  cjf®^  —  FJf.  (See  pages  75,  76.)  The  treatments  of  this 
cantus  Jirmus  with  more  movement  in  the  voices,  can  be  carried  out 
thus  : 


c./- 


g 


i^— 


=i=?S=i= 


fEtEEES 


^^^ 


W=m- 


-4=t=i 


1 

P 


MANUAL  OF  HARMONY. 


215 


P- 


m-- 


m 


I 


:e=^ 


N.  B. 


^EgEEg 


^^i 


i^^ 


i-^ 


6  6 

2        6  7     4 

4t  I    .    I    =:;=^ 


i^ 


^ 


i 


The  upward    progression  of    the  seventh  in  the  next    to  the  last 
measure  (at  N  B.)  is  caused  by  the  movement  of  the  soprano.      (See 

page  93-) 

The  treatment  of  the  cantus  Jirtmis  in  the  tenor  follows : 


e=f: 


f^EtTt- T" 


4=t 


tfe 


te 


i=?c 


^ 


-^ 


c.f. 


-(^ G>- 


1=t= 


§ite 


^F 


f^4=J 


i=4: 


^=^ 


■^—r^ 


^f 


Pfe^g^ 


;i 


u 


1 


^p 


pEt 


6 

4        3  ,6 


-^— •- 


EEfE£ 


2i6  MANUAL    OF  HARMONY. 

The  third  measure  gives  opportunity  to  speak  of  consecutive 
octaves  and  fifths  in  contrary  motiofi. 

According  to  the  principle  laid  down  heretofore,  they  are  quite  as 
faulty  as  those  in  parallel  motion,  and  it  is  especially  the  case  with 
the  octave  progressions  that  they  hamper  the  free  movement  of  the 
voices.  With  the  fifth  progressions,  however,  the  ill  effect  is  much 
mitigated  by  contrary  motion,  especially  those  which  move  towards 
each  other,  while  those  which  raow  &  from  each  other  make  the  sepa- 
ration or  want  of  connection  moi-e  perceptible.  (See  also  Ex.  430  in 
the  sixth  and  seventh  measures,  between  tenor  and  bass.) 

Compare  the  following  examples  : 


f 


^h^^i^E^^P^P^g^ 


An  examination  of  the  treatment  contained  in  this  chapter  will 
show  plainly  the  melodic  development  of  the  voices,  and  this  is  the 
reason  for  regarding  them  as  contrapuntal  labors ;  for  the  essence  of 
counterpoint,  as  distinguished  from  the  rhythmical  harmonic  form, 
requires  the  freer  melodic  leading  of  the  voices,  but  with  observance 
of  the  harmonic  laws  which  form,  so  to  speak,  its  innermost  principle. 

In  all  these  examples,  even  where  the  voices  move  in  quarter  notes, 
the  harmonic  ground-work. can  be  found,  and  thus  they  may  serve,  for 
the  present,  to  show  us  the  difference  between  the  simply  harmonic 
and  contrapuntal  treatment  of  a  given  voice.  The  more  detailed 
study  of  this  subject  belongs  properly  to  counterpoint  itself. 


CHAPTER    XXIV. 


THE    FIVK-VOICKD    MOVEMENT. 


Since  the  doubling  of  the  intervals  of  a  triad  is  necessarv  even  in  a 
four-voiced  movement,  so  also  will  it  be  necessary  in  a  greater  degree 
m  movements  for  five  or  more  voices,  and  even  with  the  chords  of  the 
seventh. 


MANUAL  OF  HARMONY. 


217 


In  the  pure  harmonic  movement,  each  voice  must  preserve  its  inde- 
pendence. To  accomplish  this,  the  intervals  best  adapted  for  doub- 
ling will  be  those  that  admit  of  a  double  progression.  This  can  take 
place,  to  a  certain  extent,  with  each  interval  of  a  chord,  but  the  sev- 
enths are  the  least  adapted  for  doubling,  except,  perhaps,  where  a 
melodic  progression  makes  it  necessary,  as  for  example,  in  passing. 

Further  remarks  follow  under  the  examples  given. 


Exercise. 


435. 


:i±S 


TTV      7r 


!t==t 


r-^-f 


^ 


% 


In  treating    this,  we    may   select,  according  to   the  position  of  the 

voices,  either  two  sopranos,  tw^o  altos  or  two  tenors. 

436.  ^ ^ 

. _^__^___ „ -^y 

Soprano, 

Alto  I. 

Alto  II. 
Tenor. 


pit 


WE 


5B 


^SE 


^=^ 


4 
2    3 


ii^ 


'^ 


■^ — &- 


1 


^ 


;b 


The  same  exercise  differently  arranged 
4-37.  ^  "^      ^  ^ ,^ 


Soprano  I. 
Soprano  II. 
Alto. 
Tenor. 

Bass. 


U 


-^ 


:l==t: 


^■ 


« 


Szg^f. 


iEEE^ 


p=ffi=^^=t 


f  I  g- 


^ 


ia 


*; 


4 
2      3 


i 


I 


I 


rr^^P^H 


i8 


MANUAL  OF  HARMONY. 


That  the  independence  of  the  voices  may  be  maintained,  two 
voices  should  not  remain  stationary  upon  one  tone,  or  in  the  octave,  if 
the  chords  change.  In  the  above  example,  in  the  first  and  second 
measures,  the  second  soprano  and  tenor  hold  the  tone  C  over  the  bar, 
but  as  the  harmony  does  not  change,  no  fault  appears,  the  chord  only 
changing  its  position. 

The  following  passage,  however  : 


may  be  corrected  thus  : 

(is 


^ 


-i — g— <&,'g 


f^ 


-'9^-^- 


=F=t= 


Remark. — This  rule,  however,  admits  of  frequent  exceptions  where  there  are  many 
parts,  because  other  relations  then  present  themselves. 


That  the  leading  of  the  voices  will  allow  the  leading  tone  to  be 
doubled,  is  shown  in  the  third  measure  of  Ex.  437,  between  the  sec- 
ond soprano  and  tenor. 

As  in  the  four-voiced  movement,  so  also  in  movements  for  five  or 
more  voices,  the  impossibility  of  avoiding  covered  fifths,  octaves  and 
unisons  will  exist  in  a  greater  degree. 

It  may  be  mentioned  again,  that  here  also  the  ojdcr  voices  must 
progress  in  pure  relations,  and  greater  freedom  be  allowed  to  the 
middle  voices  only. 

The  followin<j  example  contains  various  progressions  of  this  kind: 


4-40. 


Alto  II. 


Bass. 


m^ 


m 


S^ 


MANUAL    OF  HARMONY. 
—(2 ,—fi ^- 


g 


5[=t 


-«' — I — I =-»9- 


:t=F 


S^^ 


a 


-|g  G      V    G> (^ 1— f2 ^. 


P 


J^=F=^-F=P=^t=t 


t=f 


F 


(=2 <9 ^ <^ — &—y->^ 


^3 


:t=l=^ 


^^H 


I 


(Si e*- 


X=^ 


The  progressions  of  covered  fifths,  octaves  and  iniisons  in  this 
example  are  indicated  by  strokes.  The  open  fifth  in  the  eighth  meas- 
ure between  the  second  alto  and  bass  is  not  to  be  avoided,  since  the 
chord  of  the  diminished  seventh  can  only  with  difficulty  progress  other- 
wise when  there  are  several  parts.  The  first  and  second  alto  from  the 
eighth  measure  could  progress  thus : 


441. < 


^ 


% 


-P ^- 


^       ^  a 


220  MANUAL    OF  HARMONY. 

That  the  voices,  particularly  the  middle  ones,  must  often  cross  each 
other,  is  seen  in  the  second  and  third  measures,  between  the  second 
alto  and  tenor. 

For  practice  in  the  five-voiced  movement,  chorals  can  be  used  to 
advantage.     The  following  may  be  given  here  : 


D     C  D7     G         D7      G 


#3? 


i=t 


^ 


—      —        G     D7 


E7 


^    bo^    E 


Dt 


Fl=E^ 


^F=t=4 


G     D 


—     G     D7      G 


Exercises  in  five  or  more  voices  require  a  simple  and  natural  bass 
progression,  and  the  less  diflficult  and  artificial  it  is,  the  clearer  the 
succession  of  harmonies  will  become.  This  is  here  all  the  more 
important,  because  with  the  full  chords  and  the  necessitv  for  the  free 
movement  of  the  voices,  very  unintelligible  progressions  can  easily 
arise. 

The  beginning  of  this  exercise  here  follows : 


r-r  r  r  r  \    r  f 


^      ei 


MANUAL    OF  HARMONY.  221 

In  the  repetition,   the   following  change  in    the    harmony  can    be 

made  : 

G         G7         C  E7      «  e        a  V>       e       V.l     a 

*— ^ \ 


5E 


=t 


^- 


I 


r 


I   I 


-^ 


4==t 


gg=sg^ 


i-2 


f 


:i=rFy: 


:S=^ 


g 


I 


:t=bF=p 


i 


CHAPTER   XXV. 


THE    SIX,     SEVEN,    AND    EIGHT-VOICED    MOVEMENT. 


The  necessity  of  doubling  or  trebling  increases  with  the  number  of 
voices  added,  and  also  their  independent  movement  will  often  require 
them  to  cross  each  other.  The  simplest  harmonic  progressions  be- 
come here  the  principal  condition  of  the  possibility  of  conducting  so 
many  voices,  and  it  must  be  remembered  that  many  chords  are  not  at 
all  suited  to  this  kind  of  writing,  because  their  intervals  require  a 
fixed  progression  and  cannot  be  doubled,  notably,  the  altered  chords 
and  the  chord  of  the  diminished  seventh.  A  few  progressions  of  the 
triad  follow  here. 

Progression  to  the  second  degree : 

iced.  Five-voiced. 


^ 


9i 


I 


Six-voiced. 


Seven-voiced. 

I & 


-iS- 

zsz 


^ 


Eight-voiced. 


i 


MANUAL  OF  HARMONY. 


Progression  to  the  third  degree : 

Four-voiced.  Five-voiced.  Six-voiced.  Seven-voiced.     Eight-voiced. 


m 


^^^ 


SI; 


^z. 


Progression  to  the  fourth  degree : 

Four-voiced.  Five-voiced.  Six-voiced. 


i 


Seven-voiced.        Eight-voiced. 


^^ 


=5«? 


Progression  to  the  fifth  degree : 

Four-voiced.  Five-voiced-  Six-voiced. 


Seven -voiced.        Eight-voiced. 


9t 


^i^i=i; 


We   pass  over  further  combinations.      It  will  be  very  advantageous 
to  try  them  with  all  the  inversions. 

As  an  example  in   the  management  of  the  voices  in  six  parts,  the 
choral  under  No.  443  is  here  given : 
446. 


Soprano 
I  &  II. 


Tenor 
I&II. 


F=i 


-7S 


1       J_i: 


x,^- (S- 


'^^- 


MANUAL  OF  HARMONY. 


223 


-i         Jll          J 


■^ ^ 


^^ 


^=F=f 


W=^ 


^=t= 


:,=2 — ^ 


L_LJ L 


:t=t= 


te 


4 U 


J— 4- 


4 1 


V=^ 


t=F 


^^P 


«=-^ 


SS 


^=X 


I       I  -^       <i^ 


1^     I 

— irtg 

=^ 

— <s— 

1 

^ 

J 

I 

rt=i=p3=i^ 

1 

=F= 

^ 

—>9 ■ 

1 

— ^— 

|!31_| — 

1 ' 

-1 V— 

L       i             1 

-^ — $:— 

-V- 

1 

I 

-1 — -L-^^-^- 

-|2_ 
1 

6 

=pzd 
— ^ — 

'1 

6 

1  ~ 

— 1 — 

6 

7 

4        3 

...^ 

h^^ 

^ 

=£ 

-s^ 

FE^E^=gE^ 

-L-J- 


J V 


4-J- 


i=i 


p^^"^&s=^i 


'I — r — 1 


^t=tf 


r4^=^ 


=r:==F 


f=^ 


te= 


^^^^^^E^ 


a^ 


:^=i= 


» 


K?^ 


13 


I  I  I  I 


P^ 


:)==t: 


I       I       I       I 


;i==F 


J_J_ 


r 


E^ 


P« 


i^^S 


224 


MANUAL  OF  HARMONY. 


i*=»: 


jJEgE^g^^EE^Jg 


^ 


I       I 


J^j— J-^-4 


-gg* ^- 


1^?^ 


-^ (=2 (2Z- 


^^=F 


Since  in  polyphonic  choral  movements,  all  the  voices  are  not 
employed  at  the  same  time,  as  in  a  plain  choral  treatment,  the  har- 
mony often  appears  in  only  three  or  four  parts,  and  is  worked  up  in 
intensity  by  the  addition  of  the  others. 

The  following  examples  will  explain  this  kind  of  chorus  movement, 
and  especially  serve  to  show,  that  suspensions  and  passing  notes  can 
be  employed  in  polyhonic  work  also,  without  disadvantage  to  its  clear- 
ness and  comprehensibility. 


44-7. 


Soprano 
I&II. 


Tenor 
I&  II. 


»E^ 


5= 


^^ 


=tp=^t 


4=-^- 


U_J- 


rJc^-^-T^— ^t?a     I    g,_ 


iaE!^ 


-^- 


?^ 


MANUAL    OF  HARMONY. 


225 


J         l^.    I         I 


:^-=t5=S=l=g=a 


SB 


r=^^ 


X^^^^ 


6?:— t-^^g       g        g      fg 


^ 


tfefl 


:^=;^:^=ip=:s: 


t=^=tti 


i-^4  J 


-si <g- 


U_H-=U. 


IH 


E5 


t^P=t 


^^^^^ 


I 


9^ 


^^y-r-h^=4=^F=f 


:1M 


4-48. 

Soprano  I. 


» 


Alto  II. 


:$:^^ 


i^ 


^^^ 


'T-w- 


t=± 


f=F4^^ 


-e f- 


»=^ — r-:F=?:^gE^T^^i 


•— (-f2- 


s%=^ 


§a^^ 


^^^ 


-^^ 


^^^ 


226 


MANUAL    OF  HARMONY. 


=^^^SEP 


:p=F^ 


:t==f: 


1— i^ — -^=^^=«-*-^ 


fr 


^       -jt^.- 


-P=4= 


^ 1 


£¥ 


:t^ 


|£ 


S3 


F=^=t 


»E 


^=3=q=d: 


^EiEi^; 


3c=f 


-^ — •- 


i^ig^i 


:t=:t 


P- 


;:l===t 


^1 


»=F 


:|M^ 


^ 


^ ^ 


tt 


f=t: 


S^ 


lEi 


a£ 


iE^^EES 


e^=t^ 


S: 


95 


^ ^- 


MANUAL    OF  HARMONY. 


227 


In  eight-part  chorus  movements,  where  the  customary  four  voices 
are  usually  doubled,  the  latter  are  not  always  employed  as  eight  indi- 
pendent  voices,  which  might  easily  cause  too  great  fullness,  but  fre- 
quently two  voices  of  a  kind  are  employed  in  unison  (for  example, 
two  sopranos,  two  altos,  or  two  tenors  and  two  bases  in  unison,)  so 
that  the  harmony  often  appears  in  four,  five  and  six  parts.  We  find 
also  the  eight  voices  divided  into  two  different  choirs,  each  acting 
independently,  and  only  in  single  passages  together.  As  an  example 
of  the  peculiar  movement  which  many  of  these  parts  must  make,  the 
beginning  of  the  above  choral  is  given  here  in  eight  parts : 


Alto 
I.  &II. 


Tenor 
I.  &  II. 


Bass 
I.  &  II. 


%M 


^m^^^f 


w 


W 


J=^ 


=P==F 


iE=i 


^^t 


r-      1 

n. S— 

—<s— 

¥- 

J 

— si 

\ 

1 
— si 

prl- 

=7-t=^ 

-4- 

-4— 

15> 

1 

=p^ 

4-=f= 

^      I    - 
i^ u 

-4= 
u 

-^=: 

1 

1 
-^ f— 

-p — 

L-i— f? 

— (2_ 

-r— 

— 4- 

— s^— 

^1 

-I- — 
4 — , 

—si 

1  ~" 

\ 

i f 

H 

>fLI! 1 

=¥= 

-^ 

1 

(2. 

^ 

228  MANUAL    OF  HARMONY, 

In  polyphonic  movements  which  are  divided  into  two  different 
choirs,  the  difficulty  of  this  manner  of  writing  is  met  by  making  not 
altogether  a  tonical^  but  often  a  metrical  difference  between  the 
voices,  where  two  or  more  choirs  work  together.  It  is  always  to  be 
presumed,  however,  that  the  successions  of  harmony  shall  take  place 
in  the  simplest  manner,  and  never  by  quick  changes. 

The  above  is  generally  to  be  understood  when  we  speak  of  twelve 
or  sixteen-part  choruses,  movements,  etc.,  and  only  single  pieces  of 
Bach  are  found  where  eight  or  more  voices,  including,  however, 
instrlimental  parts,  are  treated  obligato. 

These  hints  regarding  the  polyphonic  movement  may  here  suffice, 
as  the  rest,  with  a  thorough  knowledge  of  harmony,  may  be  left  to 
personal  study.  We  may  remark  further,  however,  that  the  use  of 
the  polyphonic  form  will  be  applicable  mostly  in  compositions  for 
choirs.  In  orchestral  works  it  will  not  find  place,  as  the  taking  part 
by  so  many  instruments  of  various  kinds  would  lead  us  to  suppose. 


CHAPTER    XXVI. 

ON    THE    MUSICAL    FORMS    OF    CLOSE. 

Several  kinds  of  close  have  already  been  mentioned  on  page  33,  and 
further  remarks  followed  in  relation  to  the  authentic  close  on  pages 
41  and  56,  but  throughout  the  whole  treatise  there  has  been  no  fur- 
ther opportunity  to  revert  to  the  subject ;  therefore,  a  fuller  explana- 
tion of  these  and  other  forms  of  close  may  follow  here  : 

The  forms  of  close  are  divided,  first,  into  the  authentic  close  and 
the  plagal,  or  plagalic  close. 

The  authentic  close  has  the  formula  V — I,  the  plagal  close  IV — I 
(or  in  minor,  V — i,  iv — i),  as  has  been  shown  before.  Both  forms 
are  used  not  only  at  the  end  of  entire  compositions,  but  also  at  the 
close  of  the  principal  divisions  of  the  periods  and  their  sections.  The 
more  particular  discussion  of  this  subject  belongs  to  the  doctrine  of 
form. 

If  the  plagal  close  concludes  a  piece,  it  seldom  stands  alone,  but 


MANUAL    OF  HARMONY. 


229 

follows  the  authentic  close  ;    in   minor  it  frequently  leads  to   major, 
e.g. 


In  this  case,  as  above,  it  is  introduced  by  means  of  a  modulation. 
The  closes  (cadences)  are  also  divided  into  whole  and  half  closes,  or 
cadences.  By  the  whole  cadence  is  understood  the  same  which  is 
comprehended  under  the  authentic  cadences. 

With  the  xvhole  cadences  a  distinction  is  again  made  between  per- 
fect and  imperfect  ones. 

The  perfect  whole  cadences  are  those  in  which  the  bass  takes  the 
fundamentals  of  the  dominant  and  tonic,  and  the  soprano  the  funda- 
mental of  the  tonic,  e.  g. 

Not. 


45  1. 


i 


^ 


I 


9i=^ 


i 


If  this  is  not  the  case,  they  are  called  imperfect,  e.  g. 


fe^l 


s^^ia 


) 


i^=:^ 


S 


If  the  bass  progresses  from  the  dominant  to  another  degree,  they 
are  called  deceptive  cadences. 


453. 


m 


1=^1=^ 


:t^ 


1 


230 


MANUAL  OF  HARMONY. 


See  the  examples,  pages  91  to  94. 

The  half  cadences  have  the  form u  hi  I — V,  e.  g. 


They  also  consist  in  this,  that  the  dominant  triad  completes  the 
phrase. 

Beside  the  tonic,  chords  of  other  degrees  may  precede  the  domi- 
nant triad  in  the  formation  of  a  half  close,  e.  g. 


0    g 

rz)         1       ^. 

1 

"l~"S=q 

^j 

^■"Tl 

5 

<^      II 

«J         <^ 

VI 


Among  the  half-cadences  are  also  included  those  closes  in  the  key 
of  the  doininafit  which  are  formed  by  a  modulation  into  the  same, 
not  a  decisive  one  through  the  fundamental  position  of  the  dominant 
harmony  of  the  seventh,  but  either  through  its  inversions  or  through 
the  chord  of  the  seventh  of  the  seventh  degree,  e.  g. 


456 


G:  VI1O7 


^^m^^m 


g:  VI1O7   C:  V 


This  is  the  case,  hov^^ever,  only  in  relation  to  the  key  which  has  just 
before  been  made  use  of. 

For  the  further  understanding  of  these  kinds  of  cadences,  compare 
those  which  are  found  in  the  examples  of  this  book.  In  No.  388,  in 
the  third  and  fourth  measures,  a  half  cadence  is  found  which  is  formed 
through  II — V,  which  effects  the  close  of  the  first  section  of  the  whole 
period ;  in  the  seventh  and  eighth  measures,  however,  we  find  a  per- 
fect whole  or  authentic  cadence. 

In  Ex.  393,  in  the  third  and  fourth  measures,  is  a  half  cadence 
formed  through  I — V,  and  a  perfect  -whole.,  or  atithentic  cadence  in 
the  key  of  the  dominant  at  the  end.  (Here,  however,  there  is  no 
half  cadence.,  because  the  dominant  seventh  harmony  makes  the  mod- 
ulation complete.) 


MANUAL    OF  HARMONY.  231 

In  the  choral  under  No.  446,  the  first  strophe  ends  with  an  hnper- 
feet  whole  cadence,  the  second  with  a  perfect  tvliole  cadence,  the 
third  with  sl  half  cadence  to  e  minor  (iv — V),  the  fourth  with  a 
perfect  ivhole  cadence  in  G  major,  the  fifth  with  a  perfect  whole 
cadence  in  a  minor,  the  sixth  with  a  half  cadence  in  e  minor  (iv — 
V) ,  and  the  seventh  with  a  perfect  whole  cadence  in  G  major.  The 
application  of  the  different  cadences  is  easily  found  in  chorals ;  for 
larger  compositions  they  supply  the  means  of  boundary  and  connec- 
tion of  the  smaller  as  well  as  the  larger  movements,  and  should  there- 
fore be  used  with  much  care,  because  upon  them,  to  a  great  extent, 
depends  the  construction  of  a  piece  with  regard  to  form. 


INDEX  OF  SUBJECTS. 


Accompaniment,  figurated,  198;  harmonic  accompaniment  to  a  given  voice,  166,  189, 
209. 

After-stfikitig  oi  harmonic  tones,  137. 

Alto,  23;  alto  notes,  alto  clef,  128. 

Anticipation,  136. 

Arsis,  121,  153,  189. 

Bass,  23  ;  movement,  progression  of  the  same,  35,  36,  168,  220. 

By-tones,  harmonic,  144. 

Cadence,  59,  90;  whole,  half,  193,  228;  perfect,  imperfect,  67,  228;  in  connection  with 
modulation,  163. 

Cadence  formula,  163,  164,  165. 

Cantus firmus,  209. 

C-clef,  128. 

Chorals,  as  exercises,  191,  220. 

Chord,  21. 

Chord-formations,  accidental,  1 19. 

Chords,  altered,  45,  loi,  115;  passing,  153;  view  of  same,  113. 
"      see  also  Triads,  Chords  of  the  Seventh. 

Chord  of  the  sixth  and  fourth,  50;  the  same  in  the  formation  of  the  close,  56;  in  con- 
nection with  modulation,  158;  as  passing  chord,  154;  use  of  the  same,  168. 
"      of  the  augmented  triad,  102,  213  ;  of  the  diminished  triad,  170,  203. 

Chord  of  the  sixth  and  fifth,  63,  64,  65;  the  same  as  suspension,  204;  augmented,  109; 
in  connection  with  modulation,  161. 

Chord  of  the  second,  64,  66,  67. 

Chord  of  the  sixth,  fourth,  and  second  (see  Chord  of  the  Second). 

Chord  of  the  seventh,  21,  57  ;  chord  of  the  dominant  seventh,  57,61,  66,  91,  159  ;  essen- 
tial, 69  ;  the  same  in  passing,  153. 
"     of  the  seventh  degree  in  major,  75,  87,  100,  215. 

"      diminished,  84,  88,  96,  100;  in  connection  with  modulation,  161 ;  in  the  poly- 
phonic movement,  219. 

Chords  of  the  seventh,  connection  of  the  same  among  themselves,  8r  ;  in  connection 
with  chords  of  other  degrees,  90,  96 ;  view  of  the  same,  114. 

Chord  of  the  sixth,  50;  augmented,  106. 

Chord  of  the  thirteenth,  98,  loO,  loi. 

Chord  of  the  fourth  and  third,  chord  of  the  sixth,  fourth  and  third,  64,  65,  67. 

Chord  of  the  eleventh,  90,  98,  100. 

Chord  of  four  tones,  57  (see  Chord  of  the  Seventh). 

Chromatic  alteration,  loi. 

Consonance,  17;  complete,  incomplete,  17. 

(233) 


234  INDEX. 

Contrary  motion,  26,  1 50. 

Connection  of  chords,  25,  81,  90;  local,  inner,  35. 

Close,  33 ;  authentic,  plagal,  33. 
"    see  also  Cadence,  Whole  Close,  Half  Close,  Deceptive  Cadence. 

Closing  cadence,  59,  90. 

Closing  formula,  41,  163. 

Cross-relation,  unharmonic,  182. 

Deceptive  cadetice,  91. 

Degrees,  diatonic,  13. 

Digression  (see  Modulation). 

Dissonance,   17. 

Dominant  harmony,  C-triad,  chord  of  the  seventh  in  connection  with  modulation,  159. 

Eleventh,  14. 

Exercises,  for  practice  of  the  primary  triads  in  major,  30 ;  of  all  triads  in  major,  38  ; 
of  the  triads  in  minor,  47 ;  of  the  inversions  of  the  triads,  52  ;  of  the  chord  of 
the  dominant  seventh,  62 ;  of  the  inversions  of  the  same,  68 ;  of  the  secondary 
chords  of  the  seventh,  80:  of  the  connection  of  the  chords  of  the  seventh  among 
themselves,  82  ;  of  the  secondary  chords  of  the  seventh  in  minor,  85  ;  of  the  in- 
versions of  the  same,  89;  of  the  deceptive  cadences,  95;  of  the  secondary  chords 
of  the  seventh  in  connection  with  chords  of  other  degrees  or  keys,  97  ;  of  the  aug- 
mented triad,  104;  of  other  altered  chords,  no;  in  working  out  modulation,  117; 
of  the  suspensions,  126,  134;  of  the  harmonic  accompaniment  to  a  given  voice,, 
166,  167,  172,  179,  180,  181,  186,  187,  188,  189;  in  the  development  of  melody,, 
192;  in  the  three-voiced  movement,  202,  205,  206;  of  the  two-voiced  movement^ 
208  ;  in  the  harmonic  accompaniment  to  a  given  voice  in  melodic  development, 
209,  215  ;   in  the  five-voiced  movement,  217,  220. 

Fifteenth,  14. 

Fifth,  13,  22  ;  perfect,  15,  16;  augmented,  15,  16,  83;  diminished,  15,  16,  39,  65;  fifth 
in  the  chord  of  the  seventh,  61,  77. 

Fifth-progressions  (parallel  fifths),  26,  28,  54,  88,  109 ;  open,  30,  87  ;  covered,  30,  36,. 
124,  174,  219;  in  connection  with  passing  and  changing  notes,  148;  in  contrary 
motion,  216. 

Figuring,  47,  51,  56,  58,  125,   143. 

Fourteenth,  14. 

Fourth,  13;  perfect,  augmented,  diminished,  15,  16;  preparation  of  the  perfect  fourth 
170;  the  same  as  chord,  204,  211. 

Fourth-progressions  (fourth  parallels)  in  passing,  150,  151. 

Formation  of  the  close,  41,  56,  59. 

Fundamental  harmonies,  21  ;  chromatic  alterations  of  the  same,  lOi. 

Fundame7itaL  21  ;  in  the  chord  of  the  seventh,  60. 

Half-close  (half  cadence),  193,  228. 

Harmony,  21. 

Harmony,  tones  foreign  to  the,  119. 

Intervals,  division  of,  17;  view  of  the  same,  16,  18;  inversion  of  the  same,  18. 
"        see  also  Omission,  Reduplication. 

Intervals,  doctrine  of,  13. 

Interval,  13;  major,  perfect,  14;  minor,  augmented,  diminished,  15. 

Interval  steps  and  skips,  augmented  and  diminished,  171. 

Intervals  above,  18. 


INDEX.  235 

Intervals  below,  18. 

Inversion.,  50  ;    of  the  triads,  50 ;   of  the  chords  of  the  seventh,  63,  67,  87  (see  also  In- 
tervals). 

Leading  tone,  37,  40,  60,  84,  131,  175,  218. 

Major  triad,  22,  70. 

Melody,  its  development,  192  ;  its  rhythmical  formation,  193. 

Middle  voices,  23. 

Minor  triad,  22,  34,  70. 

Modulation,  115  ;  means  for  the  same,  156;  its  extension  and  completion,  163. 

Movement,  o\\^-\o\CG.A,  198;  two- voiced,  208  ;  three-voiced,  203;  four-voiced,  23;  five- 
voiced,  216;  six,  seven  and  eight-voiced,  221. 

Movement,  parallel,  contrary,  oblique,  26. 

Ninth,  14;  major,  minor,  15. 

Ninth,  chord  of  the,  98,  133,  143. 

Ninth-suspension,  133. 

Obliqtfc  movement,  26. 

Octave,  13;  perfect,  augmented,  diminished,  15,  16. 

Octave-progresstons  (octave  parallels),  26,  28;  open,  30,  124,  148;  covered,  30,  36,  56, 
93,  174 ;  in  contrary  motion,  216. 

Omission  of  intervals,  61,  81,  203,  208. 

Organ-point,  138. 

Outer  voices,  11.  «• 

Pass,  passing  notes,  144,  149. 

Passing  chords,  158. 

Period,  193. 

Plagal  close,  33,  43,  228. 

Position  of  the  chord,  close,  open,  dispersed,  31,  32,  129. 

Preparation,  of  the  seventh,  78  ;  of  the  suspension,  120. 

Prime,  13;  perfect,  augmented,  15,  16. 

Primary  chord  of  the  seventh,  57,  69. 

Primary  triads,  in  major,  23,  33 ;  in  minor,  42. 

Progression,  melodic,  unmelodic,  171. 

"       of  the  secondary  chords  of  the  seventh,  73,  81,  90;  see  also  resolution,  bass, 
unison,  octave,  fifth  progressions,  etc. ;  connection  of  the  chords. 

Reduplication,  of  intervals,  25,  41,  51,62,  78,  106,  123,  125,  147,  217,  221. 

Resolution,  of  the  chord  of  the  dominant  seventh,  59,  65  ;  of  the  secondary  chords  of 
the  seventh  (in  major),  71;  (in  minor)  83;  of  the  suspension,  119,  123,  131,  135. 

Scale  (see  Triads). 

Secondary  triads.,  in  major,  33  ;  in  minor,  44. 

Secondary  chords  of  the  seventh,  69,  87,  96. 

Second,  13;  major,  minor,  augmented,  15,  16. 

Second-progressions  (second  parallels),  in  passing,  150;  with  changing  notes,  1 51. 

Second,  step  of  the  augmented,  46. 

Sequence,  38. 

Seventh-progressions  (seventh  parallels),  in  passing.  150  ;  with  changing  notes,  151. 

Seventh,  13;   major,  minor,  diminished,  15,  16;    passing,  189;   preparation,  78;  the 
same  without  preparation,  79,  85,  173,  180. 

Sixth,  13;  major,  minor,  augmented,  15,  16. 

Signatures,  56. 


236 


INDEX. 


Soprano,  23;  soprano  notes,  soprano  clef,  128. 

Stationary  voices,  138,  142. 

Structure,  pure  harmonic,  24,  152. 

Style,  pure,  strict,  free,  24  ;  pure,  152. 

Subdominant  triad,  23. 

Suspension,  119,  122;  in  the  bass,  125;  from  below  upwards,  131 ;  in  several  voices, 

132,  213. 
Tenth,  14. 

Tenor,  23;  tenor  notes,  tenor  clef,  128. 
Thesis,  121,  153. 
Third,  13,  22  ;  major,  minor,  diminished,  15,  16;  in  the  chord  of  the  seventh,  171,  60, 

77;  (see  Leading  Tone). 
Thirteetith,  14. 

Thorough-bass  notation  (see  Figuring). 
Tonic  triad,  23,  157. 

Triad,  21;  major,  minor,  22  ;  dominant  triad  (in  major),  23 ;  (in  minor),  42  ;  tonic  triad, 
23;  (in  connection  with  modulation),  157  ;  subdominant  triad,  23. 
"     double-diminished,  106;  harsh-diminished,  107  ;  augmented,  45,  71,  102  ;  dimin- 
ished, 34,  39,  44,  53,  71- 
Triads  of  the  major  scale,  21,  33,  44,  113. 

"     of  the  minor  scale,  42,  44,  49,  113  ;  natural  connection  of  the  same,  22  ;  view  of 
the  same,  49,  113. 
Tritone,  77,  184. 
Twelfth,  14. 
Unison,  13. 

Unison  progressions,  28;  covered,  206,  178,  218. 
Voices,  movement  of  the,  26,  59 ;  (see  Progression,  etc.). 
Voices,  compass  of  the,  128. 
Voices,  relation  of  the,  128. 
Voices,  outer,  23;  middle  voices,  23  ;  development  of  the  accompanying  voices,  198. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


LD21-100m-9,'48(B399sl6) 


MT50.R47  1896 
C037142172 

BtRKfLt  Y  LIBRAKIIS 


III 

CD37142172 


ivi21()187    ^/  ^'° 


THE  UNIVERSITY  OF  CAUFORNIA  UBRARY 


DATE  DUE 


Music  Library 

University  of  California  at 
Berkeley 


II 


